#line 1 "main.cpp"
#include <bits/stdc++.h>
#line 1 "/home/anqooqie/.proconlib/lib/ac-library/atcoder/modint.hpp"



#line 6 "/home/anqooqie/.proconlib/lib/ac-library/atcoder/modint.hpp"
#include <type_traits>

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

#line 1 "/home/anqooqie/.proconlib/lib/ac-library/atcoder/internal_math.hpp"



#line 5 "/home/anqooqie/.proconlib/lib/ac-library/atcoder/internal_math.hpp"

#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


#line 1 "/home/anqooqie/.proconlib/lib/ac-library/atcoder/internal_type_traits.hpp"



#line 7 "/home/anqooqie/.proconlib/lib/ac-library/atcoder/internal_type_traits.hpp"

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


#line 14 "/home/anqooqie/.proconlib/lib/ac-library/atcoder/modint.hpp"

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


#line 1 "/home/anqooqie/.proconlib/tools/extended_lucas.hpp"



#line 1 "/home/anqooqie/.proconlib/tools/prime_factorization.hpp"



#line 1 "/home/anqooqie/.proconlib/tools/is_prime.hpp"



#line 1 "/home/anqooqie/.proconlib/tools/prod_mod.hpp"



namespace tools {

  template <typename T1, typename T2, typename T3>
  constexpr T3 prod_mod(const T1 x, const T2 y, const T3 m) {
    using u128 = unsigned __int128;
    u128 prod_mod = u128(x >= 0 ? x : -x) * u128(y >= 0 ? y : -y) % u128(m);
    if ((x >= 0) ^ (y >= 0)) prod_mod = u128(m) - prod_mod;
    return prod_mod;
  }
}


#line 1 "/home/anqooqie/.proconlib/tools/pow_mod.hpp"



#line 1 "/home/anqooqie/.proconlib/tools/mod.hpp"



#line 1 "/home/anqooqie/.proconlib/tools/quo.hpp"



#line 5 "/home/anqooqie/.proconlib/tools/quo.hpp"

namespace tools {

  template <typename M, typename N>
  constexpr ::std::common_type_t<M, N> quo(const M lhs, const N rhs) {
    if (lhs >= 0) {
      return lhs / rhs;
    } else {
      if (rhs >= 0) {
        return -((-lhs - 1 + rhs) / rhs);
      } else {
        return (-lhs - 1 + -rhs) / -rhs;
      }
    }
  }
}


#line 6 "/home/anqooqie/.proconlib/tools/mod.hpp"

namespace tools {

  template <typename M, typename N>
  constexpr ::std::common_type_t<M, N> mod(const M lhs, const N rhs) {
    if constexpr (::std::is_unsigned_v<M> && ::std::is_unsigned_v<N>) {
      return lhs % rhs;
    } else {
      return lhs - ::tools::quo(lhs, rhs) * rhs;
    }
  }
}


#line 6 "/home/anqooqie/.proconlib/tools/pow_mod.hpp"

namespace tools {

  template <typename T1, typename T2, typename T3>
  constexpr T3 pow_mod(const T1 x, T2 n, const T3 m) {
    if (m == 1) return 0;
    T3 r = 1;
    T3 y = ::tools::mod(x, m);
    while (n > 0) {
      if ((n & 1) > 0) {
        r = ::tools::prod_mod(r, y, m);
      }
      y = ::tools::prod_mod(y, y, m);
      n /= 2;
    }
    return r;
  }
}


#line 7 "/home/anqooqie/.proconlib/tools/is_prime.hpp"

namespace tools {

  constexpr bool is_prime(const ::std::uint_fast64_t n) {
    constexpr ::std::array<unsigned long long, 7> bases = {2, 325, 9375, 28178, 450775, 9780504, 1795265022};

    if (n <= 1) return false;
    if (n == 2) return true;
    if (n % 2 == 0) return false;

    auto d = n - 1;
    for (; d % 2 == 0; d /= 2);

    for (const auto a : bases) {
      if (a % n == 0) return true;

      auto power = d;
      auto target = ::tools::pow_mod(a, power, n);

      bool is_composite = true;
      if (target == 1) is_composite = false;
      for (; is_composite && power != n - 1; power *= 2, target = ::tools::prod_mod(target, target, n)) {
        if (target == n - 1) is_composite = false;
      }

      if (is_composite) {
        return false;
      }
    }

    return true;
  }
}


#line 1 "/home/anqooqie/.proconlib/tools/pow2.hpp"



#line 6 "/home/anqooqie/.proconlib/tools/pow2.hpp"

namespace tools {

  template <typename T, typename ::std::enable_if<::std::is_unsigned<T>::value, ::std::nullptr_t>::type = nullptr>
  constexpr T pow2(const T x) {
    return static_cast<T>(1) << x;
  }

  template <typename T, typename ::std::enable_if<::std::is_signed<T>::value, ::std::nullptr_t>::type = nullptr>
  constexpr T pow2(const T x) {
    return static_cast<T>(static_cast<typename ::std::make_unsigned<T>::type>(1) << static_cast<typename ::std::make_unsigned<T>::type>(x));
  }
}


#line 1 "/home/anqooqie/.proconlib/tools/floor_log2.hpp"



#line 1 "/home/anqooqie/.proconlib/tools/popcount.hpp"



#line 8 "/home/anqooqie/.proconlib/tools/popcount.hpp"

namespace tools {

  template <typename T>
  T popcount(T x) {
    static_assert(::std::is_integral_v<T>);
    assert(x >= 0);
    if constexpr (::std::is_signed_v<T>) {
      return static_cast<T>(::tools::popcount<::std::make_unsigned_t<T>>(x));
    } else {
      const auto log2 = [](const int w) {
        if (w == 8) return 3;
        if (w == 16) return 4;
        if (w == 32) return 5;
        if (w == 64) return 6;
        return -1;
      };
      static_assert(log2(::std::numeric_limits<T>::digits) >= 0);

      if constexpr (::std::numeric_limits<T>::digits == 8) {
        x = (x & UINT8_C(0x55)) + (x >> 1 & UINT8_C(0x55));
        x = (x & UINT8_C(0x33)) + (x >> 2 & UINT8_C(0x33));
        x = (x & UINT8_C(0x0f)) + (x >> 4 & UINT8_C(0x0f));
      } else if constexpr (::std::numeric_limits<T>::digits == 16) {
        x = (x & UINT16_C(0x5555)) + (x >> 1 & UINT16_C(0x5555));
        x = (x & UINT16_C(0x3333)) + (x >> 2 & UINT16_C(0x3333));
        x = (x & UINT16_C(0x0f0f)) + (x >> 4 & UINT16_C(0x0f0f));
        x = (x & UINT16_C(0x00ff)) + (x >> 8 & UINT16_C(0x00ff));
      } else if constexpr (::std::numeric_limits<T>::digits == 32) {
        x = (x & UINT32_C(0x55555555)) + (x >> 1 & UINT32_C(0x55555555));
        x = (x & UINT32_C(0x33333333)) + (x >> 2 & UINT32_C(0x33333333));
        x = (x & UINT32_C(0x0f0f0f0f)) + (x >> 4 & UINT32_C(0x0f0f0f0f));
        x = (x & UINT32_C(0x00ff00ff)) + (x >> 8 & UINT32_C(0x00ff00ff));
        x = (x & UINT32_C(0x0000ffff)) + (x >> 16 & UINT32_C(0x0000ffff));
      } else if constexpr (::std::numeric_limits<T>::digits == 64) {
        x = (x & UINT64_C(0x5555555555555555)) + (x >> 1 & UINT64_C(0x5555555555555555));
        x = (x & UINT64_C(0x3333333333333333)) + (x >> 2 & UINT64_C(0x3333333333333333));
        x = (x & UINT64_C(0x0f0f0f0f0f0f0f0f)) + (x >> 4 & UINT64_C(0x0f0f0f0f0f0f0f0f));
        x = (x & UINT64_C(0x00ff00ff00ff00ff)) + (x >> 8 & UINT64_C(0x00ff00ff00ff00ff));
        x = (x & UINT64_C(0x0000ffff0000ffff)) + (x >> 16 & UINT64_C(0x0000ffff0000ffff));
        x = (x & UINT64_C(0x00000000ffffffff)) + (x >> 32 & UINT64_C(0x00000000ffffffff));
      }

      return x;
    }
  }
}


#line 8 "/home/anqooqie/.proconlib/tools/floor_log2.hpp"

namespace tools {

  template <typename T>
  T floor_log2(T x) {
    static_assert(::std::is_integral_v<T>);
    assert(x > 0);
    if constexpr (::std::is_signed_v<T>) {
      return static_cast<T>(::tools::floor_log2<::std::make_unsigned_t<T>>(x));
    } else {
      const auto log2 = [](const int w) {
        if (w == 8) return 3;
        if (w == 16) return 4;
        if (w == 32) return 5;
        if (w == 64) return 6;
        return -1;
      };
      static_assert(log2(::std::numeric_limits<T>::digits) >= 0);

      x |= (x >> 1);
      x |= (x >> 2);
      x |= (x >> 4);
      if constexpr (::std::numeric_limits<T>::digits > 8) x |= (x >> 8);
      if constexpr (::std::numeric_limits<T>::digits > 16) x |= (x >> 16);
      if constexpr (::std::numeric_limits<T>::digits > 32) x |= (x >> 32);
      return ::tools::popcount(x) - static_cast<T>(1);
    }
  }
}


#line 15 "/home/anqooqie/.proconlib/tools/prime_factorization.hpp"

namespace tools {

  template <typename T>
  ::std::vector<T> prime_factorization(T n) {
    assert(1 <= n && n <= 1000000000000000000);
    ::std::vector<T> result;

    if (n == 1) return result;

    ::std::queue<::std::pair<T, T>> factors({::std::pair<T, T>(n, 1)});
    while (!factors.empty()) {
      const T factor = factors.front().first;
      const T occurrences = factors.front().second;
      factors.pop();
      if (::tools::is_prime(factor)) {
        for (T i = 0; i < occurrences; ++i) {
          result.push_back(factor);
        }
      } else {
        const T m = ::tools::pow2((::tools::floor_log2(factor) + 1) / 8);
        for (T c = 1; ; ++c) {
          const auto f = [&](T& x) {
            x = ::tools::prod_mod(x, x, factor);
            x += c;
            if (x >= factor) x -= factor;
          };
          T y = 2;
          T r = 1;
          T q = 1;
          T x, g, ys;
          do {
            x = y;
            for (T i = 0; i < r; ++i) {
              f(y);
            }
            T k = 0;
            do {
              ys = y;
              for (T i = 0; i < ::std::min(m, r - k); ++i) {
                f(y);
                q = ::tools::prod_mod(q, ::std::abs(x - y), factor);
              }
              g = ::std::gcd(q, factor);
              k += m;
            } while (k < r && g == 1);
            r *= 2;
          } while (g == 1);
          if (g == factor) {
            do {
              f(ys);
              g = ::std::gcd(::std::abs(x - ys), factor);
            } while (g == 1);
          }
          if (g < factor) {
            T h = factor / g;
            if (h < g) ::std::swap(g, h);
            T n = 1;
            while (h % g == 0) {
              h /= g;
              ++n;
            }
            factors.emplace(g, occurrences * n);
            if (h > 1) factors.emplace(h, occurrences);
            break;
          }
        }
      }
    }

    ::std::sort(result.begin(), result.end());
    return result;
  }
}


#line 1 "/home/anqooqie/.proconlib/tools/run_length.hpp"



#line 8 "/home/anqooqie/.proconlib/tools/run_length.hpp"

namespace tools {
  template <typename InputIterator, typename OutputIterator>
  void run_length(const InputIterator& begin, const InputIterator& end, OutputIterator result) {
    using T = typename ::std::iterator_traits<InputIterator>::value_type;
    if (begin == end) return;

    ::std::pair<T, ::std::size_t> prev;
    for (auto [it, breaks] = ::std::make_pair(begin, false); !breaks; breaks = it == end, it = ::std::next(it, breaks ? 0 : 1)) {
      bool flg1, flg2;
      if (it == begin) {
        flg1 = false;
        flg2 = true;
      } else if (it == end) {
        flg1 = true;
        flg2 = false;
      } else if (*it != prev.first) {
        flg1 = true;
        flg2 = true;
      } else {
        flg1 = false;
        flg2 = false;
      }
      if (flg1 || flg2) {
        if (flg1) {
          *result = prev;
          ++result;
        }
        if (flg2) {
          prev.first = *it;
          prev.second = 1;
        }
      } else {
        ++prev.second;
      }
    }
  }
}


#line 1 "/home/anqooqie/.proconlib/tools/garner.hpp"



#line 1 "/home/anqooqie/.proconlib/tools/inv_mod.hpp"



#line 1 "/home/anqooqie/.proconlib/tools/extgcd.hpp"



#line 7 "/home/anqooqie/.proconlib/tools/extgcd.hpp"

namespace tools {

  template <typename T>
  ::std::tuple<T, T, T> extgcd(T prev_r, T r) {
    T prev_s(1);
    T prev_t(0);
    T s(0);
    T t(1);
    while (r != 0) {
      const T q = ::tools::quo(prev_r, r);
      ::std::tie(prev_r, r) = ::std::make_pair(r, prev_r - q * r);
      ::std::tie(prev_s, s) = ::std::make_pair(s, prev_s - q * s);
      ::std::tie(prev_t, t) = ::std::make_pair(t, prev_t - q * t);
    }

    if (prev_r < T(0)) prev_r = -prev_r;
    return ::std::make_tuple(prev_s, prev_t, prev_r);
  }
}


#line 7 "/home/anqooqie/.proconlib/tools/inv_mod.hpp"

namespace tools {

  template <typename T1, typename T2>
  constexpr T2 inv_mod(const T1 x, const T2 m) {
    const auto [x0, y0, gcd] = ::tools::extgcd(x, m);
    assert(gcd == 1);
    return ::tools::mod(x0, m);
  }
}


#line 9 "/home/anqooqie/.proconlib/tools/garner.hpp"

// Source: https://qiita.com/drken/items/ae02240cd1f8edfc86fd
// License: unknown
// Author: drken

namespace tools {

  template <typename Iterator, typename ModType>
  ::std::pair<long long, long long> garner(const Iterator& begin, const Iterator& end, const ModType& mod) {
    ::std::vector<long long> b, m;
    for (auto it = begin; it != end; ++it) {
      b.push_back(::tools::mod(it->first, it->second));
      m.push_back(it->second);
    }

    auto lcm = 1LL;
    for (::std::size_t i = 0; i < b.size(); ++i) {
      (lcm *= m[i]) %= mod;
    }

    m.push_back(mod);
    ::std::vector<long long> coeffs(m.size(), 1);
    ::std::vector<long long> constants(m.size(), 0);
    for (::std::size_t k = 0; k < b.size(); ++k) {
      long long t = ::tools::mod((b[k] - constants[k]) * ::tools::inv_mod(coeffs[k], m[k]), m[k]);
      for (::std::size_t i = k + 1; i < m.size(); ++i) {
        (constants[i] += t * coeffs[i]) %= m[i];
        (coeffs[i] *= m[k]) %= m[i];
      }
    }

    return ::std::make_pair(constants.back(), lcm);
  }

  template <typename M, typename Iterator>
  ::std::pair<M, M> garner(const Iterator& begin, const Iterator& end) {
    const auto [y, z] = ::tools::garner(begin, end, M::mod());
    return ::std::make_pair(M::raw(y), M::raw(z));
  }
}


#line 11 "/home/anqooqie/.proconlib/tools/extended_lucas.hpp"

namespace tools {

  // Source: https://w.atwiki.jp/uwicoder/pages/2118.html#id_6779f709
  // License: unknown
  // Author: uwi

  template <class M>
  class extended_lucas {
  private:
    class prime_power {
    private:
      ::std::vector<long long> fact;
      ::std::vector<long long> ifact;

    public:
      long long p;
      long long q;
      long long P;

      prime_power(const long long p, const long long q) : p(p), q(q) {
        this->P = 1;
        for (long long i = 0; i < q; ++i) {
          this->P *= p;
        }

        this->fact.resize(this->P + 1);
        this->ifact.resize(this->P + 1);

        this->fact[0] = 1 % this->P;
        for (long long i = 1; i <= this->P; ++i) {
          this->fact[i] = this->fact[i - 1] * (i % p == 0 ? 1 : i) % this->P;
        }
        for (long long i = 0; i <= this->P; ++i) {
          long long ret = 1 % this->P;
          long long mul = this->fact[i];
          for (long long n = this->P / p * (p - 1) - 1; n > 0; n /= 2) {
            if ((n & 1) == 1) {
              ret = (ret * mul) % P;
            }
            mul = (mul * mul) % P;
          }
          this->ifact[i] = ret;
        }
      }

      long long combination(long long n, long long r) const {
        assert(0 <= r && r <= n);

        long long z = n - r;
        long long e0 = 0;
        for (long long u = n / this->p; u > 0; u /= this->p) e0 += u;
        for (long long u = r / this->p; u > 0; u /= this->p) e0 -= u;
        for (long long u = z / this->p; u > 0; u /= this->p) e0 -= u;

        long long em = 0;
        for (long long u = n / this->P; u > 0; u /= this->p) em += u;
        for (long long u = r / this->P; u > 0; u /= this->p) em -= u;
        for (long long u = z / this->P; u > 0; u /= this->p) em -= u;

        long long ret = 1 % this->P;
        while (n > 0) {
          ret = ret * this->fact[n % this->P] % this->P * this->ifact[r % this->P] % this->P * this->ifact[z % this->P] % this->P;
          n /= this->p;
          r /= this->p;
          z /= this->p;
        }
        for (long long i = 0; i < e0; ++i) {
          ret = ret * this->p % this->P;
        }
        if (!(this->p == 2 && this->q >= 3) && (em & 1) == 1) {
          ret = (this->P - ret) % this->P;
        }
        return ret;
      }
    };

    ::std::vector<::tools::extended_lucas<M>::prime_power> prime_powers;

  public:
    extended_lucas() {
      const auto prime_factors = ::tools::prime_factorization(M::mod());
      ::std::vector<::std::pair<long long, long long>> distinct_prime_factors;
      ::tools::run_length(prime_factors.begin(), prime_factors.end(), ::std::back_inserter(distinct_prime_factors));
      for (const auto& [p, q] : distinct_prime_factors) {
        this->prime_powers.emplace_back(p, q);
      }
    }
    extended_lucas(const ::tools::extended_lucas<M>&) = default;
    extended_lucas(::tools::extended_lucas<M>&&) = default;
    ~extended_lucas() = default;
    ::tools::extended_lucas<M>& operator=(const ::tools::extended_lucas<M>&) = default;
    ::tools::extended_lucas<M>& operator=(::tools::extended_lucas<M>&&) = default;

    M combination(const long long n, const long long r) const {
      if (n < 0 || r < 0 || r > n) return M::raw(0);

      ::std::vector<std::pair<long long, long long>> answers;
      answers.reserve(this->prime_powers.size());
      for (const auto& prime_power : this->prime_powers) {
        answers.emplace_back(prime_power.combination(n, r), prime_power.P);
      }

      return ::tools::garner<M>(answers.begin(), answers.end()).first;
    }
  };
}


#line 4 "main.cpp"

using ll = long long;
using mint = atcoder::static_modint<100000000>;
tools::extended_lucas<mint> cache;

int main() {
  std::cin.tie(nullptr);
  std::ios_base::sync_with_stdio(false);

  ll M, N;
  std::cin >> M >> N;
  std::cout << std::setw(8) << std::setfill('0') << cache.combination(M, N).val() << '\n';

  return 0;
}