#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

namespace hash_impl {

static constexpr unsigned long long mod = (1ULL << 61) - 1;

struct modint {
    modint() : _v(0) {}
    modint(unsigned long long v) {
        v = (v >> 61) + (v & mod);
        if (v >= mod) v -= mod;
        _v = v;
    }

    unsigned long long val() const { return _v; }

    modint& operator+=(const modint& rhs) {
        _v += rhs._v;
        if (_v >= mod) _v -= mod;
        return *this;
    }
    modint& operator-=(const modint& rhs) {
        if (_v < rhs._v) _v += mod;
        _v -= rhs._v;
        return *this;
    }
    modint& operator*=(const modint& rhs) {
        __uint128_t t = __uint128_t(_v) * rhs._v;
        t = (t >> 61) + (t & mod);
        if (t >= mod) t -= mod;
        _v = t;
        return *this;
    }
    modint& operator/=(const modint& rhs) { return *this = *this * rhs.inv(); }

    modint operator-() const { return modint() - *this; }

    modint pow(long long n) const {
        assert(0 <= n);
        modint x = *this, r = 1;
        while (n) {
            if (n & 1) r *= x;
            x *= x;
            n >>= 1;
        }
        return r;
    }
    modint inv() const { return pow(mod - 2); }

    friend modint operator+(const modint& lhs, const modint& rhs) { return modint(lhs) += rhs; }
    friend modint operator-(const modint& lhs, const modint& rhs) { return modint(lhs) -= rhs; }
    friend modint operator*(const modint& lhs, const modint& rhs) { return modint(lhs) *= rhs; }
    friend modint operator/(const modint& lhs, const modint& rhs) { return modint(lhs) /= rhs; }
    friend bool operator==(const modint& lhs, const modint& rhs) { return lhs._v == rhs._v; }
    friend bool operator!=(const modint& lhs, const modint& rhs) { return lhs._v != rhs._v; }
    friend std::ostream& operator<<(std::ostream& os, const modint& rhs) { os << rhs._v; }

  private:
    unsigned long long _v;
};

uint64_t generate_base() {
    std::mt19937_64 mt(std::chrono::steady_clock::now().time_since_epoch().count());
    std::uniform_int_distribution<uint64_t> rand(2, mod - 1);
    return rand(mt);
}

modint base(generate_base());
std::vector<modint> power{1};

modint get_pow(int n) {
    if (n < int(power.size())) return power[n];
    int m = power.size();
    power.resize(n + 1);
    for (int i = m; i <= n; i++) power[i] = power[i - 1] * base;
    return power[n];
}

};  // namespace hash_impl

struct Hash {
    using mint = hash_impl::modint;
    mint x;
    int len;

    Hash() : x(0), len(0) {}
    Hash(mint x, int len) : x(x), len(len) {}

    Hash& operator+=(const Hash& rhs) {
        x = x * hash_impl::get_pow(rhs.len) + rhs.x;
        len += rhs.len;
        return *this;
    }
    Hash operator+(const Hash& rhs) { return *this += rhs; }
    bool operator==(const Hash& rhs) { return x == rhs.x and len == rhs.len; }
};

struct ReversibleHash {
    using mint = hash_impl::modint;
    mint x, rx;
    int len;

    ReversibleHash() : x(0), rx(0), len(0) {}
    ReversibleHash(mint x) : x(x), rx(x), len(1) {}
    ReversibleHash(mint x, mint rx, int len) : x(x), rx(rx), len(len) {}

    ReversibleHash rev() const { return ReversibleHash(rx, x, len); }

    ReversibleHash operator+=(const ReversibleHash& rhs) {
        x = x * hash_impl::get_pow(rhs.len) + rhs.x;
        rx = rx + rhs.rx * hash_impl::get_pow(len);
        len += rhs.len;
        return *this;
    }
    ReversibleHash operator+(const ReversibleHash& rhs) { return *this += rhs; }
    bool operator==(const ReversibleHash& rhs) { return x == rhs.x and rx == rhs.rx and len == rhs.len; }
};

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 Mint = hash_impl::modint;

const int MAX = 1000000, MAX_BASE = 17, MAX_LEN = 30;
double LOG[MAX_BASE];
double LOG_POW[MAX_BASE][MAX_LEN];

struct S {
    int base, digit, len;
    ll val;  // 実数値が IINF 以下ならその値
    mint sum;
    Mint hash;
    double logarithm;
    S(int base, int digit, int len, ll val, mint sum, Mint hash)
        : base(base), digit(digit), len(len), val(val), sum(sum), hash(hash) {
        /*
        dd...dd
        = d * 11...11
        = d * (base^len - 1) / (base - 1)
        log(dd...dd)
        = log(d) - log(base - 1) + len * log(base) + log(1 - 1 / base^len)
        x << 1 => log(1 - x) ~ -x
        */
        logarithm = LOG[digit] - LOG[base - 1] + len * LOG[base];
        if (len < MAX_LEN) logarithm += LOG_POW[base][len];
    }
    bool operator<(const S& rhs) const {
        if (base == rhs.base) {
            if (len != rhs.len) return len < rhs.len;
            return digit < rhs.digit;
        }
        if (sum == rhs.sum and hash == rhs.hash) return true;
        if (val != IINF and rhs.val != IINF) return val < rhs.val;
        if (val != IINF) return true;
        if (rhs.val != IINF) return false;
        return logarithm < rhs.logarithm;
    }
};

template <class T> T ceil(T x, T y) {
    assert(y >= 1);
    return (x > 0 ? (x + y - 1) / y : x / y);
}
template <class T> T floor(T x, T y) {
    assert(y >= 1);
    return (x > 0 ? x / y : (x - y + 1) / y);
}

// vector<mint> tle() {
//     vector<S> cand;
//     for (int base = 2; base < MAX_BASE; base++) {
//         for (int d = 1; d < base; d++) {
//             ll cur = 0;
//             mint sum = 0;
//             Mint hash = 0;
//             int need = MAX / (base - 1) + (d < MAX % (base - 1));
//             for (int len = 1; len <= need; len++) {
//                 cur = (cur == IINF ? cur : cur >= (IINF + base - 1) / base ? IINF : min(IINF, cur * base + d));
//                 sum = sum * base + d;
//                 hash = hash * base + d;
//                 cand.emplace_back(base, d, len, cur, sum, hash);
//             }
//         }
//     }
//     sort(all(cand));
//     vector<mint> sum(MAX + 1);
//     sum[0] = 0;
//     {
//         int i = 0;
//         Mint pre = 0;
//         for (int j = 0; i < MAX; i++) {
//             while (j < int(cand.size()) and cand[j].hash == pre) j++;
//             sum[i + 1] = sum[i] + cand[j].sum;
//             pre = cand[j].hash;
//         }
//     }
//     return sum;
// }

const double eps = 1e-6;

int main() {
    ios::sync_with_stdio(false);
    cin.tie(nullptr);
    for (int i = 1; i < MAX_BASE; i++) {
        LOG[i] = log(i);
        ll cur = 1;
        for (int j = 1; j < MAX_LEN; j++) {
            cur = (cur == IINF ? cur : cur >= (IINF + i - 1) / i ? IINF : min(IINF, cur * i));
            LOG_POW[i][j] = (cur == IINF ? 0 : log(1 - 1.0 / cur));
        }
    }
    vector<pair<int, int>> nxt(MAX_BASE, {1, 1});
    vector<ll> VAL(MAX_BASE, 1);
    vector<mint> SUM(MAX_BASE, 1);
    vector<Mint> HASH(MAX_BASE, 1);
    vector<S> cand(MAX_BASE, S(2, 2, 2, 2, 2, 2));
    for (int i = 2; i < MAX_BASE; i++) cand[i] = S(i, 1, 1, VAL[i], SUM[i], HASH[i]);
    Mint pre = 0;
    mint pre_sum = 0;
    double pre_log = -10;
    vector<mint> sum(MAX + 1);
    sum[0] = 0;
    for (int i = 0; i < MAX; i++) {
        for (bool ok = false; not ok;) {
            int argmin = 2;
            for (int j = 3; j < MAX_BASE; j++) {
                if (cand[j] < cand[argmin]) {
                    argmin = j;
                }
            }
            auto [digit, len] = nxt[argmin];
            S go = cand[argmin];
            if (pre != go.hash || pre_sum != go.sum && abs(pre_log-go.logarithm) < eps) {
                sum[i + 1] = sum[i] + go.sum;
                ok = true;
            }
            pre = go.hash;
            pre_sum = go.sum;
            pre_log = go.logarithm;
            if (digit + 1 < argmin)
                nxt[argmin] = {digit + 1, len};
            else {
                nxt[argmin] = {1, len + 1};
                VAL[argmin] = (ceil(IINF, 1LL * argmin) <= VAL[argmin] ? IINF : min(VAL[argmin] * argmin + 1, IINF));
                SUM[argmin] = SUM[argmin] * argmin + 1;
                HASH[argmin] = HASH[argmin] * argmin + 1;
            }
            {
                auto [digit, len] = nxt[argmin];
                cand[argmin] = S(argmin, digit, len,
                                 (ceil(IINF, 1LL * digit) <= VAL[argmin] ? IINF : min(VAL[argmin] * digit, IINF)),
                                 SUM[argmin] * digit, HASH[argmin] * digit);
            }
        }
    }
    int t;
    cin >> t;
    for (; t--;) {
        int l, r;
        cin >> l >> r;
        mint ans = sum[r] - sum[l - 1];
        cout << ans.val() << '\n';
    }
    return 0;
}