#include <bits/stdc++.h>
#ifdef LOCAL
#include <debug.hpp>
#else
#define debug(...) void(0)
#endif

#include <type_traits>

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

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

namespace atcoder {

namespace internal {

// @param m `1 <= m`
// @return x mod m
constexpr long long safe_mod(long long x, long long m) {
    x %= m;
    if (x < 0) x += m;
    return x;
}

// Fast modular multiplication by barrett reduction
// Reference: https://en.wikipedia.org/wiki/Barrett_reduction
// NOTE: reconsider after Ice Lake
struct barrett {
    unsigned int _m;
    unsigned long long im;

    // @param m `1 <= m < 2^31`
    explicit barrett(unsigned int m) : _m(m), im((unsigned long long)(-1) / m + 1) {}

    // @return m
    unsigned int umod() const { return _m; }

    // @param a `0 <= a < m`
    // @param b `0 <= b < m`
    // @return `a * b % m`
    unsigned int mul(unsigned int a, unsigned int b) const {
        // [1] m = 1
        // a = b = im = 0, so okay

        // [2] m >= 2
        // im = ceil(2^64 / m)
        // -> im * m = 2^64 + r (0 <= r < m)
        // let z = a*b = c*m + d (0 <= c, d < m)
        // a*b * im = (c*m + d) * im = c*(im*m) + d*im = c*2^64 + c*r + d*im
        // c*r + d*im < m * m + m * im < m * m + 2^64 + m <= 2^64 + m * (m + 1) < 2^64 * 2
        // ((ab * im) >> 64) == c or c + 1
        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;
    }
};

// @param n `0 <= n`
// @param m `1 <= m`
// @return `(x ** n) % m`
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;
}

// Reference:
// M. Forisek and J. Jancina,
// Fast Primality Testing for Integers That Fit into a Machine Word
// @param n `0 <= n`
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);

// @param b `1 <= b`
// @return pair(g, x) s.t. g = gcd(a, b), xa = g (mod b), 0 <= x < b/g
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};

    // Contracts:
    // [1] s - m0 * a = 0 (mod b)
    // [2] t - m1 * a = 0 (mod b)
    // [3] s * |m1| + t * |m0| <= b
    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

        // [3]:
        // (s - t * u) * |m1| + t * |m0 - m1 * u|
        // <= s * |m1| - t * u * |m1| + t * (|m0| + |m1| * u)
        // = s * |m1| + t * |m0| <= b

        auto tmp = s;
        s = t;
        t = tmp;
        tmp = m0;
        m0 = m1;
        m1 = tmp;
    }
    // by [3]: |m0| <= b/g
    // by g != b: |m0| < b/g
    if (m0 < 0) m0 += b / s;
    return {s, m0};
}

// Compile time primitive root
// @param m must be prime
// @return primitive root (and minimum in now)
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);

// @param n `n < 2^32`
// @param m `1 <= m < 2^32`
// @return sum_{i=0}^{n-1} floor((ai + b) / m) (mod 2^64)
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;
        // y_max < m * (n + 1)
        // floor(y_max / m) <= n
        n = (unsigned long long)(y_max / m);
        b = (unsigned long long)(y_max % m);
        std::swap(m, a);
    }
    return ans;
}

}  // namespace internal

}  // namespace atcoder

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

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

namespace atcoder {

namespace internal {

// @param n `0 <= n`
// @return minimum non-negative `x` s.t. `n <= 2**x`
int ceil_pow2(int n) {
    int x = 0;
    while ((1U << x) < (unsigned int)(n)) x++;
    return x;
}

// @param n `1 <= n`
// @return minimum non-negative `x` s.t. `(n & (1 << x)) != 0`
constexpr int bsf_constexpr(unsigned int n) {
    int x = 0;
    while (!(n & (1 << x))) x++;
    return x;
}

// @param n `1 <= n`
// @return minimum non-negative `x` s.t. `(n & (1 << x)) != 0`
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

namespace atcoder {

template <class S, S (*op)(S, S), S (*e)()> struct segtree {
  public:
    segtree() : segtree(0) {}
    explicit segtree(int n) : segtree(std::vector<S>(n, e())) {}
    explicit segtree(const std::vector<S>& v) : _n(int(v.size())) {
        log = internal::ceil_pow2(_n);
        size = 1 << log;
        d = std::vector<S>(2 * size, e());
        for (int i = 0; i < _n; i++) d[size + i] = v[i];
        for (int i = size - 1; i >= 1; i--) {
            update(i);
        }
    }

    void set(int p, S x) {
        assert(0 <= p && p < _n);
        p += size;
        d[p] = x;
        for (int i = 1; i <= log; i++) update(p >> i);
    }

    S get(int p) const {
        assert(0 <= p && p < _n);
        return d[p + size];
    }

    S prod(int l, int r) const {
        assert(0 <= l && l <= r && r <= _n);
        S sml = e(), smr = e();
        l += size;
        r += size;

        while (l < r) {
            if (l & 1) sml = op(sml, d[l++]);
            if (r & 1) smr = op(d[--r], smr);
            l >>= 1;
            r >>= 1;
        }
        return op(sml, smr);
    }

    S all_prod() const { return d[1]; }

    template <bool (*f)(S)> int max_right(int l) const {
        return max_right(l, [](S x) { return f(x); });
    }
    template <class F> int max_right(int l, F f) const {
        assert(0 <= l && l <= _n);
        assert(f(e()));
        if (l == _n) return _n;
        l += size;
        S sm = e();
        do {
            while (l % 2 == 0) l >>= 1;
            if (!f(op(sm, d[l]))) {
                while (l < size) {
                    l = (2 * l);
                    if (f(op(sm, d[l]))) {
                        sm = op(sm, d[l]);
                        l++;
                    }
                }
                return l - size;
            }
            sm = op(sm, d[l]);
            l++;
        } while ((l & -l) != l);
        return _n;
    }

    template <bool (*f)(S)> int min_left(int r) const {
        return min_left(r, [](S x) { return f(x); });
    }
    template <class F> int min_left(int r, F f) const {
        assert(0 <= r && r <= _n);
        assert(f(e()));
        if (r == 0) return 0;
        r += size;
        S sm = e();
        do {
            r--;
            while (r > 1 && (r % 2)) r >>= 1;
            if (!f(op(d[r], sm))) {
                while (r < size) {
                    r = (2 * r + 1);
                    if (f(op(d[r], sm))) {
                        sm = op(d[r], sm);
                        r--;
                    }
                }
                return r + 1 - size;
            }
            sm = op(d[r], sm);
        } while ((r & -r) != r);
        return 0;
    }

  private:
    int _n, size, log;
    std::vector<S> d;

    void update(int k) { d[k] = op(d[2 * k], d[2 * k + 1]); }
};

}  // namespace atcoder

template <typename T, size_t N> struct SquareMatrix {
    std::array<std::array<T, N>, N> A;

    SquareMatrix() : A{{}} {}

    size_t size() const { return N; }

    inline const std::array<T, N>& operator[](int k) const { return A[k]; }

    inline std::array<T, N>& operator[](int k) { return A[k]; }

    static SquareMatrix I() {
        SquareMatrix res;
        for (size_t i = 0; i < N; i++) res[i][i] = 1;
        return res;
    }

    SquareMatrix& operator+=(const SquareMatrix& B) {
        for (size_t i = 0; i < N; i++) {
            for (size_t j = 0; j < N; j++) {
                (*this)[i][j] += B[i][j];
            }
        }
        return *this;
    }

    SquareMatrix& operator-=(const SquareMatrix& B) {
        for (size_t i = 0; i < N; i++) {
            for (size_t j = 0; j < N; j++) {
                (*this)[i][j] -= B[i][j];
            }
        }
        return *this;
    }

    SquareMatrix& operator*=(const SquareMatrix& B) {
        std::array<std::array<T, N>, N> C = {};
        for (size_t i = 0; i < N; i++) {
            for (size_t k = 0; k < N; k++) {
                for (size_t j = 0; j < N; j++) {
                    C[i][j] += (*this)[i][k] * B[k][j];
                }
            }
        }
        A.swap(C);
        return *this;
    }

    SquareMatrix& operator*=(const T& v) {
        for (size_t i = 0; i < N; i++) {
            for (size_t j = 0; j < N; j++) {
                (*this)[i][j] *= v;
            }
        }
        return *this;
    }

    SquareMatrix& operator/=(const T& v) {
        T inv = T(1) / v;
        for (size_t i = 0; i < N; i++) {
            for (size_t j = 0; j < N; j++) {
                (*this)[i][j] *= inv;
            }
        }
        return *this;
    }

    SquareMatrix& operator^=(long long k) {
        assert(0 <= k);
        SquareMatrix B = SquareMatrix::I();
        while (k > 0) {
            if (k & 1) B *= *this;
            *this *= *this;
            k >>= 1;
        }
        A.swap(B.A);
        return *this;
    }

    SquareMatrix operator-() const {
        SquareMatrix res;
        for (size_t i = 0; i < N; i++) {
            for (size_t j = 0; j < N; j++) {
                res[i][j] = -(*this)[i][j];
            }
        }
        return res;
    }

    SquareMatrix operator+(const SquareMatrix& B) const { return SquareMatrix(*this) += B; }

    SquareMatrix operator-(const SquareMatrix& B) const { return SquareMatrix(*this) -= B; }

    SquareMatrix operator*(const SquareMatrix& B) const { return SquareMatrix(*this) *= B; }

    SquareMatrix operator*(const T& v) const { return SquareMatrix(*this) *= v; }

    SquareMatrix operator/(const T& v) const { return SquareMatrix(*this) /= v; }

    SquareMatrix operator^(const long long k) const { return SquareMatrix(*this) ^= k; }

    bool operator==(const SquareMatrix& B) const { return A == B.A; }

    bool operator!=(const SquareMatrix& B) const { return A != B.A; }

    SquareMatrix transpose() const {
        SquareMatrix res;
        for (size_t i = 0; i < N; i++) {
            for (size_t j = 0; j < N; j++) {
                res[j][i] = (*this)[i][j];
            }
        }
        return res;
    }

    T determinant() const {
        SquareMatrix B(*this);
        T res = 1;
        for (size_t i = 0; i < N; i++) {
            int pivot = -1;
            for (size_t j = i; j < N; j++) {
                if (B[j][i] != 0) {
                    pivot = j;
                    break;
                }
            }
            if (pivot == -1) return 0;
            if (pivot != (int)i) {
                res *= -1;
                std::swap(B[i], B[pivot]);
            }
            res *= B[i][i];
            T inv = T(1) / B[i][i];
            for (size_t j = 0; j < N; j++) B[i][j] *= inv;
            for (size_t j = i + 1; j < N; j++) {
                T a = B[j][i];
                for (size_t k = 0; k < N; k++) {
                    B[j][k] -= B[i][k] * a;
                }
            }
        }
    }

    SquareMatrix inv() const {
        SquareMatrix B(*this), C = SquareMatrix::I();
        for (size_t i = 0; i < N; i++) {
            int pivot = -1;
            for (size_t j = i; j < N; j++) {
                if (B[j][i] != 0) {
                    pivot = j;
                    break;
                }
            }
            if (pivot == -1) return {};
            if (pivot != (int)i) {
                std::swap(B[i], B[pivot]);
                std::swap(C[i], C[pivot]);
            }
            T inv = T(1) / B[i][i];
            for (size_t j = 0; j < N; j++) {
                B[i][j] *= inv;
                C[i][j] *= inv;
            }
            for (size_t j = 0; j < N; j++) {
                if (j == i) continue;
                T a = B[j][i];
                for (size_t k = 0; k < N; k++) {
                    B[j][k] -= B[i][k] * a;
                    C[j][k] -= C[i][k] * a;
                }
            }
        }
        return C;
    }

    friend std::ostream& operator<<(std::ostream& os, const SquareMatrix& p) {
        os << "[(" << N << " * " << N << " Matrix)";
        os << "\n[columun sums: ";
        for (size_t j = 0; j < N; j++) {
            T sum = 0;
            for (size_t i = 0; i < N; i++) sum += p[i][j];
            ;
            os << sum << (j + 1 < N ? "," : "");
        }
        os << "]";
        for (size_t i = 0; i < N; i++) {
            os << "\n[";
            for (size_t j = 0; j < N; j++) os << p[i][j] << (j + 1 < N ? "," : "");
            os << "]";
        }
        os << "]\n";
        return os;
    }
};

namespace atcoder {

template <class T, internal::is_modint_t<T>* = nullptr> std::istream& operator>>(std::istream& is, T& x) {
    int v;
    is >> v;
    x = T::raw(v);
    return is;
}

template <class T, internal::is_modint_t<T>* = nullptr> std::ostream& operator<<(std::ostream& os, const T& x) {
    return os << x.val();
}

}  // namespace atcoder

using namespace std;

typedef long long ll;
#define all(x) begin(x), end(x)
constexpr int INF = (1 << 30) - 1;
constexpr long long IINF = (1LL << 60) - 1;
constexpr int dx[4] = {1, 0, -1, 0}, dy[4] = {0, 1, 0, -1};

template <class T> istream& operator>>(istream& is, vector<T>& v) {
    for (auto& x : v) is >> x;
    return is;
}

template <class T> ostream& operator<<(ostream& os, const vector<T>& v) {
    auto sep = "";
    for (const auto& x : v) os << exchange(sep, " ") << x;
    return os;
}

template <class T, class U = T> bool chmin(T& x, U&& y) { return y < x and (x = forward<U>(y), true); }

template <class T, class U = T> bool chmax(T& x, U&& y) { return x < y and (x = forward<U>(y), true); }

template <class T> void mkuni(vector<T>& v) {
    sort(begin(v), end(v));
    v.erase(unique(begin(v), end(v)), end(v));
}

template <class T> int lwb(const vector<T>& v, const T& x) { return lower_bound(begin(v), end(v), x) - begin(v); }

using mint = atcoder::modint998244353;
using SM = SquareMatrix<mint, 3>;
using AR = array<mint, 3>;

SM op(SM l, SM r) { return l * r; }

SM e() { return SM::I(); }

SM vec_to_mat(const AR& v) {
    SM res;
    res[0] = {0, -v[2], v[1]};
    res[1] = {v[2], 0, -v[0]};
    res[2] = {-v[1], v[0], 0};
    return res;
}

AR mul(const SM& m, const AR& v) {
    AR res = {0, 0, 0};
    for (int i = 0; i < 3; i++) {
        for (int j = 0; j < 3; j++) {
            res[i] += m[i][j] * v[j];
        }
    }
    return res;
}

int main() {
    ios::sync_with_stdio(false);
    cin.tie(nullptr);
    int n, q;
    cin >> n >> q;
    vector<int> leaf(n), xx(n), yy(n), zz(n);
    vector<vector<int>> G(n);
    for (int i = 0; i < n; i++) {
        char c;
        cin >> c;
        if (c == 'x') {
            leaf[i] = 0;
            int l, r;
            cin >> l >> r;
            G[i].emplace_back(--l);
            G[i].emplace_back(--r);
        } else {
            leaf[i] = 1;
            cin >> xx[i] >> yy[i] >> zz[i];
        }
    }

    vector<int> par(n), dep(n), sub(n), vid(n), vid_inv(n), head(n);
    int sgn = 1;
    {
        auto dfs_sz = [&](auto self, int v) -> void {
            sub[v] = 1;
            if (leaf[v]) return;
            for (int& u : G[v]) {
                par[u] = v;
                dep[u] = dep[v] + 1;
                self(self, u);
                sub[v] += sub[u];
            }
            if (sub[G[v][1]] > sub[G[v][0]]) {
                swap(G[v][0], G[v][1]);
                sgn *= -1;
            }
        };
        int time = 0;
        auto dfs_hld = [&](auto self, int v) -> void {
            vid[v] = time++;
            if (leaf[v]) return;
            head[G[v][0]] = head[v];
            head[G[v][1]] = G[v][1];
            for (int i = 0; i < 2; i++) {
                int u = G[v][i];
                head[u] = (i == 0 ? head[v] : u);
                self(self, u);
            }
        };
        head[0] = 0;
        par[0] = -1;
        dep[0] = 0;
        dfs_sz(dfs_sz, 0);
        dfs_hld(dfs_hld, 0);
        for (int i = 0; i < n; i++) vid_inv[vid[i]] = i;
    }
    vector<AR> root(n, {0, 0, 0}),  // v が heavy path の root ならそこでの vector の値
        tail(n, {0, 0, 0});         // heavy path の先での vector の値
    vector<atcoder::segtree<SM, op, e>> seg(n);  // v を root とする heavy path から生える作用素を載せたセグ木（これに
                                                 // tail[v] をかけることで root[v] が計算できる）
    vector<int> cnt(n, 0);
    for (int i = 0; i < n; i++) cnt[head[i]]++;
    for (int i = 0; i < n; i++) {
        if (cnt[i] > 1) {
            seg[i] = atcoder::segtree<SM, op, e>(cnt[i] - 1);
        }
    }
    auto update = [&](int v, int x, int y, int z) {
        {
            int p = head[v];
            tail[p] = {x, y, z};
            root[p] = mul(seg[p].all_prod(), tail[p]);
            v = p;
        }
        while (v != 0) {
            int p = par[v], pp = head[p];
            int idx = dep[p] - dep[pp];
            seg[pp].set(idx, vec_to_mat(root[v]));
            root[pp] = mul(seg[pp].all_prod(), tail[pp]);
            v = pp;
        }
    };
    for (int i = 0; i < n; i++) {
        if (leaf[i]) {
            update(i, xx[i], yy[i], zz[i]);
        }
    }
    auto query = [&]() -> AR {
        auto res = root[0];
        for (int i = 0; i < 3; i++) res[i] *= sgn;
        return res;
    };

    for (; q--;) {
        int v, x, y, z;
        cin >> v >> x >> y >> z;
        update(--v, x, y, z);
        auto ans = query();
        cout << ans[0].val() << ' ' << ans[1].val() << ' ' << ans[2].val() << '\n';
    }
    return 0;
}