#include <bits/stdc++.h>
using namespace std;
typedef long long ll;
using ull = unsigned long long;
typedef pair<ll, ll> pll;
typedef vector<ll> vll;
typedef vector<pll> vpll;
template <class T> using pqmin = priority_queue<T, vector<T>, greater<T>>;
template <class T> using pqmax = priority_queue<T>;
const ll inf = LLONG_MAX / 3;
const ll dx[] = {0, 1, 0, -1, 1, -1, 1, -1};
const ll dy[] = {1, 0, -1, 0, 1, 1, -1, -1};
#define mp make_pair
#define pb push_back
#define eb emplace_back
#define fi first
#define se second
#define all(x) x.begin(), x.end()
#define si(x) ll(x.size())
#define rep(i, n) for(ll i = 0; i < n; i++)
#define per(i, n) for(ll i = n - 1; i >= 0; i--)
#define rng(i, l, r) for(ll i = l; i < r; i++)
#define gnr(i, l, r) for(ll i = r - 1; i >= l; i--)
#define fore(i, a) for(auto &&i : a)
#define fore2(a, b, v) for(auto &&[a, b] : v)
#define fore3(a, b, c, v) for(auto &&[a, b, c] : v)
template <class T> bool chmin(T &a, const T &b) {
    if(a <= b) return 0;
    a = b;
    return 1;
}
template <class T> bool chmax(T &a, const T &b) {
    if(a >= b) return 0;
    a = b;
    return 1;
}
template <class T, class U> bool chmin(T &a, const U &b) { return chmin(a, (T)b); }
template <class T, class U> bool chmax(T &a, const U &b) { return chmax(a, (T)b); }
#define LL(...)                                                                                                                                                \
    ll __VA_ARGS__;                                                                                                                                            \
    in(__VA_ARGS__)
#define STR(...)                                                                                                                                               \
    string __VA_ARGS__;                                                                                                                                        \
    in(__VA_ARGS__)
#define CHR(...)                                                                                                                                               \
    char __VA_ARGS__;                                                                                                                                          \
    in(__VA_ARGS__)
#define vec(type, name, ...) vector<type> name(__VA_ARGS__)
#define VEC(type, name, size)                                                                                                                                  \
    vector<type> name(size);                                                                                                                                   \
    in(name)
#define VLL(name, size)                                                                                                                                        \
    vector<ll> name(size);                                                                                                                                     \
    in(name)
#define vv(type, name, h, ...) vector<vector<type>> name(h, vector<type>(__VA_ARGS__))
#define VV(type, name, h, w)                                                                                                                                   \
    vector<vector<type>> name(h, vector<type>(w));                                                                                                             \
    in(name)
#define vvv(type, name, h, w, ...) vector<vector<vector<type>>> name(h, vector<vector<type>>(w, vector<type>(__VA_ARGS__)))
#define SUM(...) accumulate(all(__VA_ARGS__), 0LL)
template <class T> auto min(const T &a) { return *min_element(all(a)); }
template <class T> auto max(const T &a) { return *max_element(all(a)); }
template <class T, class F = less<>> void sor(T &a, F b = F{}) { sort(all(a), b); }
template <class T> void uniq(T &a) {
    sor(a);
    a.erase(unique(all(a)), end(a));
}
void outb(bool x) { cout << (x ? "Yes" : "No") << "\n"; }
ll max(int x, ll y) { return max((ll)x, y); }
ll max(ll x, int y) { return max(x, (ll)y); }
int min(int x, ll y) { return min((ll)x, y); }
int min(ll x, int y) { return min(x, (ll)y); }
#define lb(c, x) distance((c).begin(), lower_bound(all(c), (x)))
#define lbg(c, x) distance((c).begin(), lower_bound(all(c), (x), greater{}))
#define ub(c, x) distance((c).begin(), upper_bound(all(c), (x)))
#define ubg(c, x) distance((c).begin(), upper_bound(all(c), (x), greater{}))
ll gcd(ll a, ll b) { return (b ? gcd(b, a % b) : a); }
vector<pll> factor(ull x) {
    vector<pll> ans;
    for(ull i = 2; i * i <= x; i++)
        if(x % i == 0) {
            ans.push_back({i, 1});
            while((x /= i) % i == 0) ans.back().second++;
        }
    if(x != 1) ans.push_back({x, 1});
    return ans;
}
vector<ll> divisor(ull x) {
    vector<ll> ans;
    for(ull i = 1; i * i <= x; i++)
        if(x % i == 0) ans.push_back(i);
    per(i, ans.size() - (ans.back() * ans.back() == x)) ans.push_back(x / ans[i]);
    return ans;
}
vll prime_table(ll n) {
    vec(ll, isp, n + 1, 1);
    vll res;
    rng(i, 2, n + 1) if(isp[i]) {
        res.pb(i);
        for(ll j = i * i; j <= n; j += i) isp[j] = 0;
    }
    return res;
}

template <class T, class S> pair<T, S> operator-(const pair<T, S> &x) { return pair<T, S>(-x.first, -x.second); }
template <class T, class S> pair<T, S> operator-(const pair<T, S> &x, const pair<T, S> &y) { return pair<T, S>(x.fi - y.fi, x.se - y.se); }
template <class T, class S> pair<T, S> operator+(const pair<T, S> &x, const pair<T, S> &y) { return pair<T, S>(x.fi + y.fi, x.se + y.se); }
template <class T> pair<T, T> operator&(const pair<T, T> &l, const pair<T, T> &r) { return pair<T, T>(max(l.fi, r.fi), min(l.se, r.se)); }
template <class T, class S> pair<T, S> operator+=(pair<T, S> &l, const pair<T, S> &r) { return l = l + r; }
template <class T, class S> pair<T, S> operator-=(pair<T, S> &l, const pair<T, S> &r) { return l = l - r; }
template <class T> bool intersect(const pair<T, T> &l, const pair<T, T> &r) { return (l.se < r.se ? r.fi < l.se : l.fi < r.se); }

template <class T> vector<T> &operator++(vector<T> &v) {
    fore(e, v) e++;
    return v;
}
template <class T> vector<T> operator++(vector<T> &v, int) {
    auto res = v;
    fore(e, v) e++;
    return res;
}
template <class T> vector<T> &operator--(vector<T> &v) {
    fore(e, v) e--;
    return v;
}
template <class T> vector<T> operator--(vector<T> &v, int) {
    auto res = v;
    fore(e, v) e--;
    return res;
}
template <class T> vector<T> &operator+=(vector<T> &l, const vector<T> &r) {
    fore(e, r) l.eb(e);
    return l;
}

template <class... Ts> void in(Ts &...t);
[[maybe_unused]] void print() {}
template <class T, class... Ts> void print(const T &t, const Ts &...ts);
template <class... Ts> void out(const Ts &...ts) {
    print(ts...);
    cout << '\n';
}
namespace IO {
#define VOID(a) decltype(void(a))
struct S {
    S() {
        cin.tie(nullptr)->sync_with_stdio(0);
        fixed(cout).precision(12);
    }
} S;
template <int I> struct P : P<I - 1> {};
template <> struct P<0> {};
template <class T> void i(T &t) { i(t, P<3>{}); }
void i(vector<bool>::reference t, P<3>) {
    int a;
    i(a);
    t = a;
}
template <class T> auto i(T &t, P<2>) -> VOID(cin >> t) { cin >> t; }
template <class T> auto i(T &t, P<1>) -> VOID(begin(t)) {
    for(auto &&x : t) i(x);
}
template <class T, size_t... idx> void ituple(T &t, index_sequence<idx...>) { in(get<idx>(t)...); }
template <class T> auto i(T &t, P<0>) -> VOID(tuple_size<T>{}) { ituple(t, make_index_sequence<tuple_size<T>::value>{}); }
template <class T> void o(const T &t) { o(t, P<4>{}); }
template <size_t N> void o(const char (&t)[N], P<4>) { cout << t; }
template <class T, size_t N> void o(const T (&t)[N], P<3>) {
    o(t[0]);
    for(size_t i = 1; i < N; i++) {
        o(' ');
        o(t[i]);
    }
}
template <class T> auto o(const T &t, P<2>) -> VOID(cout << t) { cout << t; }
template <class T> auto o(const T &t, P<1>) -> VOID(begin(t)) {
    bool first = 1;
    for(auto &&x : t) {
        if(first)
            first = 0;
        else
            o(' ');
        o(x);
    }
}
template <class T, size_t... idx> void otuple(const T &t, index_sequence<idx...>) { print(get<idx>(t)...); }
template <class T> auto o(T &t, P<0>) -> VOID(tuple_size<T>{}) { otuple(t, make_index_sequence<tuple_size<T>::value>{}); }
#undef VOID
} // namespace IO
#define unpack(a)                                                                                                                                              \
    (void)initializer_list<int> { (a, 0)... }
template <class... Ts> void in(Ts &...t) { unpack(IO::i(t)); }
template <class T, class... Ts> void print(const T &t, const Ts &...ts) {
    IO::o(t);
    unpack(IO::o((cout << ' ', ts)));
}
#undef unpack
#ifdef _MSC_VER
#include <intrin.h>
#endif

namespace atcoder {

namespace internal {

int ceil_pow2(int n) {
    int x = 0;
    while((1U << x) < (unsigned int)(n)) x++;
    return x;
}

constexpr int bsf_constexpr(unsigned int n) {
    int x = 0;
    while(!(n & (1 << x))) x++;
    return x;
}

int bsf(unsigned int n) {
#ifdef _MSC_VER
    unsigned long index;
    _BitScanForward(&index, n);
    return index;
#else
    return __builtin_ctz(n);
#endif
}

} // namespace internal

} // namespace atcoder

#include <cassert>
#include <numeric>
#include <type_traits>

#ifdef _MSC_VER
#include <intrin.h>
#endif

#include <utility>

#ifdef _MSC_VER
#include <intrin.h>
#endif

namespace atcoder {

namespace internal {

constexpr long long safe_mod(long long x, long long m) {
    x %= m;
    if(x < 0) x += m;
    return x;
}

struct barrett {
    unsigned int _m;
    unsigned long long im;

    explicit barrett(unsigned int m) : _m(m), im((unsigned long long)(-1) / m + 1) {}

    unsigned int umod() const { return _m; }

    unsigned int mul(unsigned int a, unsigned int b) const {

        unsigned long long z = a;
        z *= b;
#ifdef _MSC_VER
        unsigned long long x;
        _umul128(z, im, &x);
#else
        unsigned long long x = (unsigned long long)(((unsigned __int128)(z)*im) >> 64);
#endif
        unsigned int v = (unsigned int)(z - x * _m);
        if(_m <= v) v += _m;
        return v;
    }
};

constexpr long long pow_mod_constexpr(long long x, long long n, int m) {
    if(m == 1) return 0;
    unsigned int _m = (unsigned int)(m);
    unsigned long long r = 1;
    unsigned long long y = safe_mod(x, m);
    while(n) {
        if(n & 1) r = (r * y) % _m;
        y = (y * y) % _m;
        n >>= 1;
    }
    return r;
}

constexpr bool is_prime_constexpr(int n) {
    if(n <= 1) return false;
    if(n == 2 || n == 7 || n == 61) return true;
    if(n % 2 == 0) return false;
    long long d = n - 1;
    while(d % 2 == 0) d /= 2;
    constexpr long long bases[3] = {2, 7, 61};
    for(long long a : bases) {
        long long t = d;
        long long y = pow_mod_constexpr(a, t, n);
        while(t != n - 1 && y != 1 && y != n - 1) {
            y = y * y % n;
            t <<= 1;
        }
        if(y != n - 1 && t % 2 == 0) { return false; }
    }
    return true;
}
template <int n> constexpr bool is_prime = is_prime_constexpr(n);

constexpr std::pair<long long, long long> inv_gcd(long long a, long long b) {
    a = safe_mod(a, b);
    if(a == 0) return {b, 0};

    long long s = b, t = a;
    long long m0 = 0, m1 = 1;

    while(t) {
        long long u = s / t;
        s -= t * u;
        m0 -= m1 * u; // |m1 * u| <= |m1| * s <= b

        auto tmp = s;
        s = t;
        t = tmp;
        tmp = m0;
        m0 = m1;
        m1 = tmp;
    }
    if(m0 < 0) m0 += b / s;
    return {s, m0};
}

constexpr int primitive_root_constexpr(int m) {
    if(m == 2) return 1;
    if(m == 167772161) return 3;
    if(m == 469762049) return 3;
    if(m == 754974721) return 11;
    if(m == 998244353) return 3;
    int divs[20] = {};
    divs[0] = 2;
    int cnt = 1;
    int x = (m - 1) / 2;
    while(x % 2 == 0) x /= 2;
    for(int i = 3; (long long)(i)*i <= x; i += 2) {
        if(x % i == 0) {
            divs[cnt++] = i;
            while(x % i == 0) { x /= i; }
        }
    }
    if(x > 1) { divs[cnt++] = x; }
    for(int g = 2;; g++) {
        bool ok = true;
        for(int i = 0; i < cnt; i++) {
            if(pow_mod_constexpr(g, (m - 1) / divs[i], m) == 1) {
                ok = false;
                break;
            }
        }
        if(ok) return g;
    }
}
template <int m> constexpr int primitive_root = primitive_root_constexpr(m);

unsigned long long floor_sum_unsigned(unsigned long long n, unsigned long long m, unsigned long long a, unsigned long long b) {
    unsigned long long ans = 0;
    while(true) {
        if(a >= m) {
            ans += n * (n - 1) / 2 * (a / m);
            a %= m;
        }
        if(b >= m) {
            ans += n * (b / m);
            b %= m;
        }

        unsigned long long y_max = a * n + b;
        if(y_max < m) break;
        n = (unsigned long long)(y_max / m);
        b = (unsigned long long)(y_max % m);
        std::swap(m, a);
    }
    return ans;
}

} // namespace internal

} // namespace atcoder

#include <cassert>
#include <numeric>
#include <type_traits>

namespace atcoder {

namespace internal {

#ifndef _MSC_VER
template <class T>
using is_signed_int128 =
    typename std::conditional<std::is_same<T, __int128_t>::value || std::is_same<T, __int128>::value, std::true_type, std::false_type>::type;

template <class T>
using is_unsigned_int128 =
    typename std::conditional<std::is_same<T, __uint128_t>::value || std::is_same<T, unsigned __int128>::value, std::true_type, std::false_type>::type;

template <class T> using make_unsigned_int128 = typename std::conditional<std::is_same<T, __int128_t>::value, __uint128_t, unsigned __int128>;

template <class T>
using is_integral =
    typename std::conditional<std::is_integral<T>::value || is_signed_int128<T>::value || is_unsigned_int128<T>::value, std::true_type, std::false_type>::type;

template <class T>
using is_signed_int =
    typename std::conditional<(is_integral<T>::value && std::is_signed<T>::value) || is_signed_int128<T>::value, std::true_type, std::false_type>::type;

template <class T>
using is_unsigned_int =
    typename std::conditional<(is_integral<T>::value && std::is_unsigned<T>::value) || is_unsigned_int128<T>::value, std::true_type, std::false_type>::type;

template <class T>
using to_unsigned = typename std::conditional<is_signed_int128<T>::value, make_unsigned_int128<T>,
                                              typename std::conditional<std::is_signed<T>::value, std::make_unsigned<T>, std::common_type<T>>::type>::type;

#else

template <class T> using is_integral = typename std::is_integral<T>;

template <class T> using is_signed_int = typename std::conditional<is_integral<T>::value && std::is_signed<T>::value, std::true_type, std::false_type>::type;

template <class T>
using is_unsigned_int = typename std::conditional<is_integral<T>::value && std::is_unsigned<T>::value, std::true_type, std::false_type>::type;

template <class T> using to_unsigned = typename std::conditional<is_signed_int<T>::value, std::make_unsigned<T>, std::common_type<T>>::type;

#endif

template <class T> using is_signed_int_t = std::enable_if_t<is_signed_int<T>::value>;

template <class T> using is_unsigned_int_t = std::enable_if_t<is_unsigned_int<T>::value>;

template <class T> using to_unsigned_t = typename to_unsigned<T>::type;

} // namespace internal

} // namespace atcoder

namespace atcoder {

namespace internal {

struct modint_base {};
struct static_modint_base : modint_base {};

template <class T> using is_modint = std::is_base_of<modint_base, T>;
template <class T> using is_modint_t = std::enable_if_t<is_modint<T>::value>;

} // namespace internal

template <int m, std::enable_if_t<(1 <= m)> * = nullptr> struct static_modint : internal::static_modint_base {
    using mint = static_modint;

  public:
    static constexpr int mod() { return m; }
    static mint raw(int v) {
        mint x;
        x._v = v;
        return x;
    }

    static_modint() : _v(0) {}
    template <class T, internal::is_signed_int_t<T> * = nullptr> static_modint(T v) {
        long long x = (long long)(v % (long long)(umod()));
        if(x < 0) x += umod();
        _v = (unsigned int)(x);
    }
    template <class T, internal::is_unsigned_int_t<T> * = nullptr> static_modint(T v) { _v = (unsigned int)(v % umod()); }

    unsigned int val() const { return _v; }

    mint &operator++() {
        _v++;
        if(_v == umod()) _v = 0;
        return *this;
    }
    mint &operator--() {
        if(_v == 0) _v = umod();
        _v--;
        return *this;
    }
    mint operator++(int) {
        mint result = *this;
        ++*this;
        return result;
    }
    mint operator--(int) {
        mint result = *this;
        --*this;
        return result;
    }

    mint &operator+=(const mint &rhs) {
        _v += rhs._v;
        if(_v >= umod()) _v -= umod();
        return *this;
    }
    mint &operator-=(const mint &rhs) {
        _v -= rhs._v;
        if(_v >= umod()) _v += umod();
        return *this;
    }
    mint &operator*=(const mint &rhs) {
        unsigned long long z = _v;
        z *= rhs._v;
        _v = (unsigned int)(z % umod());
        return *this;
    }
    mint &operator/=(const mint &rhs) { return *this = *this * rhs.inv(); }

    mint operator+() const { return *this; }
    mint operator-() const { return mint() - *this; }

    mint pow(long long n) const {
        assert(0 <= n);
        mint x = *this, r = 1;
        while(n) {
            if(n & 1) r *= x;
            x *= x;
            n >>= 1;
        }
        return r;
    }
    mint inv() const {
        if(prime) {
            assert(_v);
            return pow(umod() - 2);
        } else {
            auto eg = internal::inv_gcd(_v, m);
            assert(eg.first == 1);
            return eg.second;
        }
    }

    friend mint operator+(const mint &lhs, const mint &rhs) { return mint(lhs) += rhs; }
    friend mint operator-(const mint &lhs, const mint &rhs) { return mint(lhs) -= rhs; }
    friend mint operator*(const mint &lhs, const mint &rhs) { return mint(lhs) *= rhs; }
    friend mint operator/(const mint &lhs, const mint &rhs) { return mint(lhs) /= rhs; }
    friend bool operator==(const mint &lhs, const mint &rhs) { return lhs._v == rhs._v; }
    friend bool operator!=(const mint &lhs, const mint &rhs) { return lhs._v != rhs._v; }

  private:
    unsigned int _v;
    static constexpr unsigned int umod() { return m; }
    static constexpr bool prime = internal::is_prime<m>;
};

template <int id> struct dynamic_modint : internal::modint_base {
    using mint = dynamic_modint;

  public:
    static int mod() { return (int)(bt.umod()); }
    static void set_mod(int m) {
        assert(1 <= m);
        bt = internal::barrett(m);
    }
    static mint raw(int v) {
        mint x;
        x._v = v;
        return x;
    }

    dynamic_modint() : _v(0) {}
    template <class T, internal::is_signed_int_t<T> * = nullptr> dynamic_modint(T v) {
        long long x = (long long)(v % (long long)(mod()));
        if(x < 0) x += mod();
        _v = (unsigned int)(x);
    }
    template <class T, internal::is_unsigned_int_t<T> * = nullptr> dynamic_modint(T v) { _v = (unsigned int)(v % mod()); }

    unsigned int val() const { return _v; }

    mint &operator++() {
        _v++;
        if(_v == umod()) _v = 0;
        return *this;
    }
    mint &operator--() {
        if(_v == 0) _v = umod();
        _v--;
        return *this;
    }
    mint operator++(int) {
        mint result = *this;
        ++*this;
        return result;
    }
    mint operator--(int) {
        mint result = *this;
        --*this;
        return result;
    }

    mint &operator+=(const mint &rhs) {
        _v += rhs._v;
        if(_v >= umod()) _v -= umod();
        return *this;
    }
    mint &operator-=(const mint &rhs) {
        _v += mod() - rhs._v;
        if(_v >= umod()) _v -= umod();
        return *this;
    }
    mint &operator*=(const mint &rhs) {
        _v = bt.mul(_v, rhs._v);
        return *this;
    }
    mint &operator/=(const mint &rhs) { return *this = *this * rhs.inv(); }

    mint operator+() const { return *this; }
    mint operator-() const { return mint() - *this; }

    mint pow(long long n) const {
        assert(0 <= n);
        mint x = *this, r = 1;
        while(n) {
            if(n & 1) r *= x;
            x *= x;
            n >>= 1;
        }
        return r;
    }
    mint inv() const {
        auto eg = internal::inv_gcd(_v, mod());
        assert(eg.first == 1);
        return eg.second;
    }

    friend mint operator+(const mint &lhs, const mint &rhs) { return mint(lhs) += rhs; }
    friend mint operator-(const mint &lhs, const mint &rhs) { return mint(lhs) -= rhs; }
    friend mint operator*(const mint &lhs, const mint &rhs) { return mint(lhs) *= rhs; }
    friend mint operator/(const mint &lhs, const mint &rhs) { return mint(lhs) /= rhs; }
    friend bool operator==(const mint &lhs, const mint &rhs) { return lhs._v == rhs._v; }
    friend bool operator!=(const mint &lhs, const mint &rhs) { return lhs._v != rhs._v; }

  private:
    unsigned int _v;
    static internal::barrett bt;
    static unsigned int umod() { return bt.umod(); }
};
template <int id> internal::barrett dynamic_modint<id>::bt(998244353);

using modint998244353 = static_modint<998244353>;
using modint1000000007 = static_modint<1000000007>;
using modint = dynamic_modint<-1>;

namespace internal {

template <class T> using is_static_modint = std::is_base_of<internal::static_modint_base, T>;

template <class T> using is_static_modint_t = std::enable_if_t<is_static_modint<T>::value>;

template <class> struct is_dynamic_modint : public std::false_type {};
template <int id> struct is_dynamic_modint<dynamic_modint<id>> : public std::true_type {};

template <class T> using is_dynamic_modint_t = std::enable_if_t<is_dynamic_modint<T>::value>;

} // namespace internal

} // namespace atcoder

namespace atcoder {

namespace internal {

template <class mint, int g = internal::primitive_root<mint::mod()>, internal::is_static_modint_t<mint> * = nullptr> struct fft_info {
    static constexpr int rank2 = bsf_constexpr(mint::mod() - 1);
    std::array<mint, rank2 + 1> root;  // root[i]^(2^i) == 1
    std::array<mint, rank2 + 1> iroot; // root[i] * iroot[i] == 1

    std::array<mint, std::max(0, rank2 - 2 + 1)> rate2;
    std::array<mint, std::max(0, rank2 - 2 + 1)> irate2;

    std::array<mint, std::max(0, rank2 - 3 + 1)> rate3;
    std::array<mint, std::max(0, rank2 - 3 + 1)> irate3;

    fft_info() {
        root[rank2] = mint(g).pow((mint::mod() - 1) >> rank2);
        iroot[rank2] = root[rank2].inv();
        for(int i = rank2 - 1; i >= 0; i--) {
            root[i] = root[i + 1] * root[i + 1];
            iroot[i] = iroot[i + 1] * iroot[i + 1];
        }

        {
            mint prod = 1, iprod = 1;
            for(int i = 0; i <= rank2 - 2; i++) {
                rate2[i] = root[i + 2] * prod;
                irate2[i] = iroot[i + 2] * iprod;
                prod *= iroot[i + 2];
                iprod *= root[i + 2];
            }
        }
        {
            mint prod = 1, iprod = 1;
            for(int i = 0; i <= rank2 - 3; i++) {
                rate3[i] = root[i + 3] * prod;
                irate3[i] = iroot[i + 3] * iprod;
                prod *= iroot[i + 3];
                iprod *= root[i + 3];
            }
        }
    }
};

template <class mint, internal::is_static_modint_t<mint> * = nullptr> void butterfly(std::vector<mint> &a) {
    int n = int(a.size());
    int h = internal::ceil_pow2(n);

    static const fft_info<mint> info;

    int len = 0; // a[i, i+(n>>len), i+2*(n>>len), ..] is transformed
    while(len < h) {
        if(h - len == 1) {
            int p = 1 << (h - len - 1);
            mint rot = 1;
            for(int s = 0; s < (1 << len); s++) {
                int offset = s << (h - len);
                for(int i = 0; i < p; i++) {
                    auto l = a[i + offset];
                    auto r = a[i + offset + p] * rot;
                    a[i + offset] = l + r;
                    a[i + offset + p] = l - r;
                }
                if(s + 1 != (1 << len)) rot *= info.rate2[bsf(~(unsigned int)(s))];
            }
            len++;
        } else {
            int p = 1 << (h - len - 2);
            mint rot = 1, imag = info.root[2];
            for(int s = 0; s < (1 << len); s++) {
                mint rot2 = rot * rot;
                mint rot3 = rot2 * rot;
                int offset = s << (h - len);
                for(int i = 0; i < p; i++) {
                    auto mod2 = 1ULL * mint::mod() * mint::mod();
                    auto a0 = 1ULL * a[i + offset].val();
                    auto a1 = 1ULL * a[i + offset + p].val() * rot.val();
                    auto a2 = 1ULL * a[i + offset + 2 * p].val() * rot2.val();
                    auto a3 = 1ULL * a[i + offset + 3 * p].val() * rot3.val();
                    auto a1na3imag = 1ULL * mint(a1 + mod2 - a3).val() * imag.val();
                    auto na2 = mod2 - a2;
                    a[i + offset] = a0 + a2 + a1 + a3;
                    a[i + offset + 1 * p] = a0 + a2 + (2 * mod2 - (a1 + a3));
                    a[i + offset + 2 * p] = a0 + na2 + a1na3imag;
                    a[i + offset + 3 * p] = a0 + na2 + (mod2 - a1na3imag);
                }
                if(s + 1 != (1 << len)) rot *= info.rate3[bsf(~(unsigned int)(s))];
            }
            len += 2;
        }
    }
}

template <class mint, internal::is_static_modint_t<mint> * = nullptr> void butterfly_inv(std::vector<mint> &a) {
    int n = int(a.size());
    int h = internal::ceil_pow2(n);

    static const fft_info<mint> info;

    int len = h; // a[i, i+(n>>len), i+2*(n>>len), ..] is transformed
    while(len) {
        if(len == 1) {
            int p = 1 << (h - len);
            mint irot = 1;
            for(int s = 0; s < (1 << (len - 1)); s++) {
                int offset = s << (h - len + 1);
                for(int i = 0; i < p; i++) {
                    auto l = a[i + offset];
                    auto r = a[i + offset + p];
                    a[i + offset] = l + r;
                    a[i + offset + p] = (unsigned long long)(mint::mod() + l.val() - r.val()) * irot.val();
                    ;
                }
                if(s + 1 != (1 << (len - 1))) irot *= info.irate2[bsf(~(unsigned int)(s))];
            }
            len--;
        } else {
            int p = 1 << (h - len);
            mint irot = 1, iimag = info.iroot[2];
            for(int s = 0; s < (1 << (len - 2)); s++) {
                mint irot2 = irot * irot;
                mint irot3 = irot2 * irot;
                int offset = s << (h - len + 2);
                for(int i = 0; i < p; i++) {
                    auto a0 = 1ULL * a[i + offset + 0 * p].val();
                    auto a1 = 1ULL * a[i + offset + 1 * p].val();
                    auto a2 = 1ULL * a[i + offset + 2 * p].val();
                    auto a3 = 1ULL * a[i + offset + 3 * p].val();

                    auto a2na3iimag = 1ULL * mint((mint::mod() + a2 - a3) * iimag.val()).val();

                    a[i + offset] = a0 + a1 + a2 + a3;
                    a[i + offset + 1 * p] = (a0 + (mint::mod() - a1) + a2na3iimag) * irot.val();
                    a[i + offset + 2 * p] = (a0 + a1 + (mint::mod() - a2) + (mint::mod() - a3)) * irot2.val();
                    a[i + offset + 3 * p] = (a0 + (mint::mod() - a1) + (mint::mod() - a2na3iimag)) * irot3.val();
                }
                if(s + 1 != (1 << (len - 2))) irot *= info.irate3[bsf(~(unsigned int)(s))];
            }
            len -= 2;
        }
    }
}

template <class mint, internal::is_static_modint_t<mint> * = nullptr>
std::vector<mint> convolution_naive(const std::vector<mint> &a, const std::vector<mint> &b) {
    int n = int(a.size()), m = int(b.size());
    std::vector<mint> ans(n + m - 1);
    if(n < m) {
        for(int j = 0; j < m; j++) {
            for(int i = 0; i < n; i++) { ans[i + j] += a[i] * b[j]; }
        }
    } else {
        for(int i = 0; i < n; i++) {
            for(int j = 0; j < m; j++) { ans[i + j] += a[i] * b[j]; }
        }
    }
    return ans;
}

template <class mint, internal::is_static_modint_t<mint> * = nullptr> std::vector<mint> convolution_fft(std::vector<mint> a, std::vector<mint> b) {
    int n = int(a.size()), m = int(b.size());
    int z = 1 << internal::ceil_pow2(n + m - 1);
    a.resize(z);
    internal::butterfly(a);
    b.resize(z);
    internal::butterfly(b);
    for(int i = 0; i < z; i++) { a[i] *= b[i]; }
    internal::butterfly_inv(a);
    a.resize(n + m - 1);
    mint iz = mint(z).inv();
    for(int i = 0; i < n + m - 1; i++) a[i] *= iz;
    return a;
}

} // namespace internal

template <class mint, internal::is_static_modint_t<mint> * = nullptr> std::vector<mint> convolution(std::vector<mint> &&a, std::vector<mint> &&b) {
    int n = int(a.size()), m = int(b.size());
    if(!n || !m) return {};
    if(std::min(n, m) <= 60) return convolution_naive(a, b);
    return internal::convolution_fft(a, b);
}

template <class mint, internal::is_static_modint_t<mint> * = nullptr> std::vector<mint> convolution(const std::vector<mint> &a, const std::vector<mint> &b) {
    int n = int(a.size()), m = int(b.size());
    if(!n || !m) return {};
    if(std::min(n, m) <= 60) return convolution_naive(a, b);
    return internal::convolution_fft(a, b);
}

template <unsigned int mod = 998244353, class T, std::enable_if_t<internal::is_integral<T>::value> * = nullptr>
std::vector<T> convolution(const std::vector<T> &a, const std::vector<T> &b) {
    int n = int(a.size()), m = int(b.size());
    if(!n || !m) return {};

    using mint = static_modint<mod>;
    std::vector<mint> a2(n), b2(m);
    for(int i = 0; i < n; i++) { a2[i] = mint(a[i]); }
    for(int i = 0; i < m; i++) { b2[i] = mint(b[i]); }
    auto c2 = convolution(move(a2), move(b2));
    std::vector<T> c(n + m - 1);
    for(int i = 0; i < n + m - 1; i++) { c[i] = c2[i].val(); }
    return c;
}

std::vector<long long> convolution_ll(const std::vector<long long> &a, const std::vector<long long> &b) {
    int n = int(a.size()), m = int(b.size());
    if(!n || !m) return {};

    static constexpr unsigned long long MOD1 = 754974721; // 2^24
    static constexpr unsigned long long MOD2 = 167772161; // 2^25
    static constexpr unsigned long long MOD3 = 469762049; // 2^26
    static constexpr unsigned long long M2M3 = MOD2 * MOD3;
    static constexpr unsigned long long M1M3 = MOD1 * MOD3;
    static constexpr unsigned long long M1M2 = MOD1 * MOD2;
    static constexpr unsigned long long M1M2M3 = MOD1 * MOD2 * MOD3;

    static constexpr unsigned long long i1 = internal::inv_gcd(MOD2 * MOD3, MOD1).second;
    static constexpr unsigned long long i2 = internal::inv_gcd(MOD1 * MOD3, MOD2).second;
    static constexpr unsigned long long i3 = internal::inv_gcd(MOD1 * MOD2, MOD3).second;

    auto c1 = convolution<MOD1>(a, b);
    auto c2 = convolution<MOD2>(a, b);
    auto c3 = convolution<MOD3>(a, b);

    std::vector<long long> c(n + m - 1);
    for(int i = 0; i < n + m - 1; i++) {
        unsigned long long x = 0;
        x += (c1[i] * i1) % MOD1 * M2M3;
        x += (c2[i] * i2) % MOD2 * M1M3;
        x += (c3[i] * i3) % MOD3 * M1M2;
        long long diff = c1[i] - internal::safe_mod((long long)(x), (long long)(MOD1));
        if(diff < 0) diff += MOD1;
        static constexpr unsigned long long offset[5] = {0, 0, M1M2M3, 2 * M1M2M3, 3 * M1M2M3};
        x -= offset[diff % 5];
        c[i] = x;
    }

    return c;
}

} // namespace atcoder

using namespace atcoder;
using mint = modint998244353;
using vmint = vector<mint>;

// combination mod prime
// https://youtu.be/8uowVvQ_-Mo?t=6002
// https://youtu.be/Tgd_zLfRZOQ?t=9928
struct modinv {
    int n;
    vector<mint> d;
    modinv() : n(2), d({0, 1}) {}
    mint operator()(int i) {
        while(n <= i) d.push_back(-d[mint::mod() % n] * (mint::mod() / n)), ++n;
        return d[i];
    }
    mint operator[](int i) const { return d[i]; }
} invs;
struct modfact {
    int n;
    vector<mint> d;
    modfact() : n(2), d({1, 1}) {}
    mint operator()(int i) {
        while(n <= i) d.push_back(d.back() * n), ++n;
        return d[i];
    }
    mint operator[](int i) const { return d[i]; }
} facts;
struct modfactinv {
    int n;
    vector<mint> d;
    modfactinv() : n(2), d({1, 1}) {}
    mint operator()(int i) {
        while(n <= i) d.push_back(d.back() * invs(n)), ++n;
        return d[i];
    }
    mint operator[](int i) const { return d[i]; }
} ifacts;
mint comb(int n, int k) {
    if(n < k || k < 0) return 0;
    return facts(n) * ifacts(k) * ifacts(n - k);
}

// https://nyaannyaan.github.io/library/hashmap/hashmap.hpp
namespace HashMapImpl {
using u32 = uint32_t;
using u64 = uint64_t;

template <typename Key, typename Data> struct HashMapBase;

template <typename Key, typename Data> struct itrB : iterator<bidirectional_iterator_tag, Data, ptrdiff_t, Data *, Data &> {
    using base = iterator<bidirectional_iterator_tag, Data, ptrdiff_t, Data *, Data &>;
    using ptr = typename base::pointer;
    using ref = typename base::reference;

    u32 i;
    HashMapBase<Key, Data> *p;

    explicit constexpr itrB() : i(0), p(nullptr) {}
    explicit constexpr itrB(u32 _i, HashMapBase<Key, Data> *_p) : i(_i), p(_p) {}
    explicit constexpr itrB(u32 _i, const HashMapBase<Key, Data> *_p) : i(_i), p(const_cast<HashMapBase<Key, Data> *>(_p)) {}
    friend void swap(itrB &l, itrB &r) { swap(l.i, r.i), swap(l.p, r.p); }
    friend bool operator==(const itrB &l, const itrB &r) { return l.i == r.i; }
    friend bool operator!=(const itrB &l, const itrB &r) { return l.i != r.i; }
    const ref operator*() const { return const_cast<const HashMapBase<Key, Data> *>(p)->data[i]; }
    ref operator*() { return p->data[i]; }
    ptr operator->() const { return &(p->data[i]); }

    itrB &operator++() {
        assert(i != p->cap && "itr::operator++()");
        do {
            i++;
            if(i == p->cap) break;
            if(p->flag[i] == true && p->dflag[i] == false) break;
        } while(true);
        return (*this);
    }
    itrB operator++(int) {
        itrB it(*this);
        ++(*this);
        return it;
    }
    itrB &operator--() {
        do {
            i--;
            if(p->flag[i] == true && p->dflag[i] == false) break;
            assert(i != 0 && "itr::operator--()");
        } while(true);
        return (*this);
    }
    itrB operator--(int) {
        itrB it(*this);
        --(*this);
        return it;
    }
};

template <typename Key, typename Data> struct HashMapBase {
    using u32 = uint32_t;
    using u64 = uint64_t;
    using iterator = itrB<Key, Data>;
    using itr = iterator;

  protected:
    template <typename K> inline u64 randomized(const K &key) const { return u64(key) ^ r; }

    template <typename K, enable_if_t<is_same<K, Key>::value, nullptr_t> = nullptr, enable_if_t<is_integral<K>::value, nullptr_t> = nullptr>
    inline u32 inner_hash(const K &key) const {
        return (randomized(key) * 11995408973635179863ULL) >> shift;
    }
    template <typename K, enable_if_t<is_same<K, Key>::value, nullptr_t> = nullptr, enable_if_t<is_integral<decltype(K::first)>::value, nullptr_t> = nullptr,
              enable_if_t<is_integral<decltype(K::second)>::value, nullptr_t> = nullptr>
    inline u32 inner_hash(const K &key) const {
        u64 a = randomized(key.first), b = randomized(key.second);
        a *= 11995408973635179863ULL;
        b *= 10150724397891781847ULL;
        return (a + b) >> shift;
    }
    template <typename K, enable_if_t<is_same<K, Key>::value, nullptr_t> = nullptr,
              enable_if_t<is_integral<typename K::value_type>::value, nullptr_t> = nullptr>
    inline u32 inner_hash(const K &key) const {
        static constexpr u64 mod = (1LL << 61) - 1;
        static constexpr u64 base = 950699498548472943ULL;
        u64 res = 0;
        for(auto &elem : key) {
            __uint128_t x = __uint128_t(res) * base + (randomized(elem) & mod);
            res = (x & mod) + (x >> 61);
        }
        __uint128_t x = __uint128_t(res) * base;
        res = (x & mod) + (x >> 61);
        if(res >= mod) res -= mod;
        return res >> (shift - 3);
    }

    template <typename D = Data, enable_if_t<is_same<D, Key>::value, nullptr_t> = nullptr> inline u32 hash(const D &dat) const { return inner_hash(dat); }
    template <typename D = Data, enable_if_t<is_same<decltype(D::first), Key>::value, nullptr_t> = nullptr> inline u32 hash(const D &dat) const {
        return inner_hash(dat.first);
    }

    template <typename D = Data, enable_if_t<is_same<D, Key>::value, nullptr_t> = nullptr> inline Key dtok(const D &dat) const { return dat; }
    template <typename D = Data, enable_if_t<is_same<decltype(D::first), Key>::value, nullptr_t> = nullptr> inline Key dtok(const D &dat) const {
        return dat.first;
    }

    void reallocate(u32 ncap) {
        vector<Data> ndata(ncap);
        vector<bool> nf(ncap);
        shift = 64 - __lg(ncap);
        for(u32 i = 0; i < cap; i++) {
            if(flag[i] == true && dflag[i] == false) {
                u32 h = hash(data[i]);
                while(nf[h]) h = (h + 1) & (ncap - 1);
                ndata[h] = move(data[i]);
                nf[h] = true;
            }
        }
        data.swap(ndata);
        flag.swap(nf);
        cap = ncap;
        dflag.resize(cap);
        fill(std::begin(dflag), std::end(dflag), false);
    }

    inline bool extend_rate(u32 x) const { return x * 2 >= cap; }

    inline bool shrink_rate(u32 x) const { return HASHMAP_DEFAULT_SIZE < cap && x * 10 <= cap; }

    inline void extend() { reallocate(cap << 1); }

    inline void shrink() { reallocate(cap >> 1); }

  public:
    u32 cap, s;
    vector<Data> data;
    vector<bool> flag, dflag;
    u32 shift;
    static u64 r;
    static constexpr uint32_t HASHMAP_DEFAULT_SIZE = 4;

    explicit HashMapBase() : cap(HASHMAP_DEFAULT_SIZE), s(0), data(cap), flag(cap), dflag(cap), shift(64 - __lg(cap)) {}

    itr begin() const {
        u32 h = 0;
        while(h != cap) {
            if(flag[h] == true && dflag[h] == false) break;
            h++;
        }
        return itr(h, this);
    }
    itr end() const { return itr(this->cap, this); }

    friend itr begin(const HashMapBase &h) { return h.begin(); }
    friend itr end(const HashMapBase &h) { return h.end(); }

    itr find(const Key &key) const {
        u32 h = inner_hash(key);
        while(true) {
            if(flag[h] == false) return this->end();
            if(dtok(data[h]) == key) {
                if(dflag[h] == true) return this->end();
                return itr(h, this);
            }
            h = (h + 1) & (cap - 1);
        }
    }

    bool contain(const Key &key) const { return find(key) != this->end(); }

    itr insert(const Data &d) {
        u32 h = hash(d);
        while(true) {
            if(flag[h] == false) {
                if(extend_rate(s + 1)) {
                    extend();
                    h = hash(d);
                    continue;
                }
                data[h] = d;
                flag[h] = true;
                ++s;
                return itr(h, this);
            }
            if(dtok(data[h]) == dtok(d)) {
                if(dflag[h] == true) {
                    data[h] = d;
                    dflag[h] = false;
                    ++s;
                }
                return itr(h, this);
            }
            h = (h + 1) & (cap - 1);
        }
    }

    // tips for speed up :
    // if return value is unnecessary, make argument_2 false.
    itr erase(itr it, bool get_next = true) {
        if(it == this->end()) return this->end();
        s--;
        if(shrink_rate(s)) {
            Data d = data[it.i];
            shrink();
            it = find(dtok(d));
        }
        int ni = (it.i + 1) & (cap - 1);
        if(this->flag[ni]) {
            this->dflag[it.i] = true;
        } else {
            this->flag[it.i] = false;
        }
        if(get_next) ++it;
        return it;
    }

    itr erase(const Key &key) { return erase(find(key)); }

    bool empty() const { return s == 0; }

    int size() const { return s; }

    void clear() {
        fill(std::begin(flag), std::end(flag), false);
        fill(std::begin(dflag), std::end(dflag), false);
        s = 0;
    }

    void reserve(int n) {
        if(n <= 0) return;
        n = 1 << min(23, __lg(n) + 2);
        if(cap < u32(n)) reallocate(n);
    }
};

template <typename Key, typename Data>
uint64_t HashMapBase<Key, Data>::r = chrono::duration_cast<chrono::nanoseconds>(chrono::high_resolution_clock::now().time_since_epoch()).count();

} // namespace HashMapImpl

/**
 * @brief Hash Map(base)　(ハッシュマップ・基底クラス)
 */

template <typename Key, typename Val> struct HashMap : HashMapImpl::HashMapBase<Key, pair<Key, Val>> {
    using base = typename HashMapImpl::HashMapBase<Key, pair<Key, Val>>;
    using HashMapImpl::HashMapBase<Key, pair<Key, Val>>::HashMapBase;
    using Data = pair<Key, Val>;

    Val &operator[](const Key &k) {
        typename base::u32 h = base::inner_hash(k);
        while(true) {
            if(base::flag[h] == false) {
                if(base::extend_rate(base::s + 1)) {
                    base::extend();
                    h = base::hash(k);
                    continue;
                }
                base::data[h].first = k;
                base::data[h].second = Val();
                base::flag[h] = true;
                ++base::s;
                return base::data[h].second;
            }
            if(base::data[h].first == k) {
                if(base::dflag[h] == true) base::data[h].second = Val();
                return base::data[h].second;
            }
            h = (h + 1) & (base::cap - 1);
        }
    }

    typename base::itr emplace(const Key &key, const Val &val) { return base::insert(Data(key, val)); }
};

/*
 * @brief ハッシュマップ(連想配列)
 * @docs docs/hashmap/hashmap.md
 **/

template <typename Key> struct HashSet : HashMapImpl::HashMapBase<Key, Key> {
    using HashMapImpl::HashMapBase<Key, Key>::HashMapBase;
};

/*
 * @brief ハッシュセット(集合)
 * @docs docs/hashmap/hashset.md
 **/

void solve() {
    LL(n, k);
    vv(ll, g, n);
    rep(i, n - 1) {
        ll a, b;
        cin >> a >> b;
        a--, b--;
        g[a].pb(b);
        g[b].pb(a);
    }
    auto dfs = [&](auto &&dfs, ll x, ll p, vector<pair<ll, mint>> &ret) -> void {
        HashMap<ll, mint> dp;
        dp[1] = 1;
        fore(y, g[x]) if(y != p) {
            vector<pair<ll, mint>> v;
            HashMap<ll, mint> cop;
            dfs(dfs, y, x, v);
            fore2(a, val1, dp) fore2(b, val2, v) {
                ll c = a + b;
                if(c <= k + 1) cop[c] += val1 * val2;
            }
            swap(dp, cop);
        }
        if((dp[k + 1] + dp[k]).val() != 0) ret.eb(0, dp[k + 1] + dp[k]);
        fore2(c, val, dp) {
            if(c <= k) { ret.eb(c, val); }
        }
    };
    vector<pair<ll, mint>> v;
    dfs(dfs, 0, -1, v);
		mint ans=0;
		fore2(c,val,v)if(c==0){
			ans=val;
		}
    out(ans.val());
}
int main() {
    cin.tie(0);
    ios::sync_with_stdio(0);
    ll t;
    cin >> t;
    while(t--) solve();
}