#line 1 "main.cpp"
#include <bits/stdc++.h>
#define rep(i, n) for (int i = 0; i < (int)(n); i++)
#define rrep(i, n) for (int i = (int)(n - 1); i >= 0; i--)
#define all(x) (x).begin(), (x).end()
#define sz(x) int(x.size())
using namespace std;
using ll = long long;
constexpr int INF = 1e9;
constexpr ll LINF = 1e18;
string YesNo(bool cond) {
    return cond ? "Yes" : "No";
}
string YESNO(bool cond) {
    return cond ? "YES" : "NO";
}
template <class T>
bool chmax(T& a, const T& b) {
    if (a < b) {
        a = b;
        return true;
    }
    return false;
}
template <class T>
bool chmin(T& a, const T& b) {
    if (b < a) {
        a = b;
        return true;
    }
    return false;
}
template <typename T, class F>
T bisect(T ok, T ng, const F& f) {
    while (abs(ok - ng) > 1) {
        T mid = min(ok, ng) + (abs(ok - ng) >> 1);
        (f(mid) ? ok : ng) = mid;
    }
    return ok;
}
template <typename T, class F>
T bisect_double(T ok, T ng, const F& f, int iter = 100) {
    while (iter--) {
        T mid = (ok + ng) / 2;
        (f(mid) ? ok : ng) = mid;
    }
    return ok;
}
template <class T>
vector<T> make_vec(size_t a) {
    return vector<T>(a);
}
template <class T, class... Ts>
auto make_vec(size_t a, Ts... ts) {
    return vector<decltype(make_vec<T>(ts...))>(a, make_vec<T>(ts...));
}
template <typename T>
istream& operator>>(istream& is, vector<T>& v) {
    for (int i = 0; i < int(v.size()); i++) {
        is >> v[i];
    }
    return is;
}
template <typename T>
ostream& operator<<(ostream& os, const vector<T>& v) {
    for (int i = 0; i < int(v.size()); i++) {
        os << v[i];
        if (i < sz(v) - 1) os << ' ';
    }
    return os;
}
#line 1 "/Users/gyouzasushi/kyopro/library/atcoder/modint.hpp"



#line 6 "/Users/gyouzasushi/kyopro/library/atcoder/modint.hpp"
#include <type_traits>

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

#line 1 "/Users/gyouzasushi/kyopro/library/atcoder/internal_math.hpp"



#line 5 "/Users/gyouzasushi/kyopro/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 "/Users/gyouzasushi/kyopro/library/atcoder/internal_type_traits.hpp"



#line 7 "/Users/gyouzasushi/kyopro/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 "/Users/gyouzasushi/kyopro/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 72 "main.cpp"
using mint = atcoder::modint998244353;
#line 3 "/Users/gyouzasushi/kyopro/library/math/binomial_coefficient.hpp"
template <typename mint>
struct factorial_table {
    static mint val(int i) {
        ensure(i);
        return facts[i];
    }
    static mint inv(int i) {
        ensure(i);
        return ifacts[i];
    }
    static void ensure(int n) {
        int sz = facts.size();
        if (sz > n) return;
        if (n < sz << 1) n = sz << 1;
        facts.resize(n + 1);
        ifacts.resize(n + 1);
        for (int i = sz; i <= n; i++) facts[i] = facts[i - 1] * i;
        ifacts[n] = facts[n].inv();
        for (int i = n; i >= sz; i--) ifacts[i - 1] = ifacts[i] * i;
    }

private:
    static inline std::vector<mint> facts{1};
    static inline std::vector<mint> ifacts{1};
};

template <typename mint>
struct binomial_coefficient {
    using facts = factorial_table<mint>;
    static mint C(int n, int k) {
        if (n < 0 || n < k || k < 0) return 0;
        return facts::val(n) * facts::inv(n - k) * facts::inv(k);
    }
    static mint P(int n, int k) {
        if (n < 0 || n < k || k < 0) return 0;
        return facts::val(n) * facts::inv(n - k);
    }
    static mint H(int n, int k) {
        if (n < 0 || k < 0) return 0;
        if (k == 0) return 1;
        return C(n + k - 1, k);
    }
};

#line 1 "/Users/gyouzasushi/kyopro/library/atcoder/math.hpp"



#line 8 "/Users/gyouzasushi/kyopro/library/atcoder/math.hpp"

#line 10 "/Users/gyouzasushi/kyopro/library/atcoder/math.hpp"

namespace atcoder {

long long pow_mod(long long x, long long n, int m) {
    assert(0 <= n && 1 <= m);
    if (m == 1) return 0;
    internal::barrett bt((unsigned int)(m));
    unsigned int r = 1, y = (unsigned int)(internal::safe_mod(x, m));
    while (n) {
        if (n & 1) r = bt.mul(r, y);
        y = bt.mul(y, y);
        n >>= 1;
    }
    return r;
}

long long inv_mod(long long x, long long m) {
    assert(1 <= m);
    auto z = internal::inv_gcd(x, m);
    assert(z.first == 1);
    return z.second;
}

// (rem, mod)
std::pair<long long, long long> crt(const std::vector<long long>& r,
                                    const std::vector<long long>& m) {
    assert(r.size() == m.size());
    int n = int(r.size());
    // Contracts: 0 <= r0 < m0
    long long r0 = 0, m0 = 1;
    for (int i = 0; i < n; i++) {
        assert(1 <= m[i]);
        long long r1 = internal::safe_mod(r[i], m[i]), m1 = m[i];
        if (m0 < m1) {
            std::swap(r0, r1);
            std::swap(m0, m1);
        }
        if (m0 % m1 == 0) {
            if (r0 % m1 != r1) return {0, 0};
            continue;
        }
        // assume: m0 > m1, lcm(m0, m1) >= 2 * max(m0, m1)

        // (r0, m0), (r1, m1) -> (r2, m2 = lcm(m0, m1));
        // r2 % m0 = r0
        // r2 % m1 = r1
        // -> (r0 + x*m0) % m1 = r1
        // -> x*u0*g = r1-r0 (mod u1*g) (u0*g = m0, u1*g = m1)
        // -> x = (r1 - r0) / g * inv(u0) (mod u1)

        // im = inv(u0) (mod u1) (0 <= im < u1)
        long long g, im;
        std::tie(g, im) = internal::inv_gcd(m0, m1);

        long long u1 = (m1 / g);
        // |r1 - r0| < (m0 + m1) <= lcm(m0, m1)
        if ((r1 - r0) % g) return {0, 0};

        // u1 * u1 <= m1 * m1 / g / g <= m0 * m1 / g = lcm(m0, m1)
        long long x = (r1 - r0) / g % u1 * im % u1;

        // |r0| + |m0 * x|
        // < m0 + m0 * (u1 - 1)
        // = m0 + m0 * m1 / g - m0
        // = lcm(m0, m1)
        r0 += x * m0;
        m0 *= u1;  // -> lcm(m0, m1)
        if (r0 < 0) r0 += m0;
    }
    return {r0, m0};
}

long long floor_sum(long long n, long long m, long long a, long long b) {
    assert(0 <= n && n < (1LL << 32));
    assert(1 <= m && m < (1LL << 32));
    unsigned long long ans = 0;
    if (a < 0) {
        unsigned long long a2 = internal::safe_mod(a, m);
        ans -= 1ULL * n * (n - 1) / 2 * ((a2 - a) / m);
        a = a2;
    }
    if (b < 0) {
        unsigned long long b2 = internal::safe_mod(b, m);
        ans -= 1ULL * n * ((b2 - b) / m);
        b = b2;
    }
    return ans + internal::floor_sum_unsigned(n, m, a, b);
}

}  // namespace atcoder


#line 4 "/Users/gyouzasushi/kyopro/library/math/factorize.hpp"
long long modmul(long long x, long long y, long long mod) {
    using i128 = __int128_t;
    return (long long)(i128(x) * i128(y) % i128(mod));
}
long long modpow(long long a, long long n, long long mod) {
    long long ret = 1;
    while (n > 0) {
        if (n & 1) ret = modmul(ret, a, mod);
        a = modmul(a, a, mod);
        n >>= 1;
    }
    return ret;
}
long long rho(long long n) {
    long long z = 0;
    auto f = [&](long long x) -> long long {
        long long ret = modmul(x, x, n) + z;
        if (ret == n) return 0;
        return ret;
    };
    while (true) {
        long long x = ++z;
        long long y = f(x);
        while (true) {
            long long d = std::gcd(std::abs(x - y), n);
            if (d == n) break;
            if (d > 1) return d;
            x = f(x);
            y = f(f(y));
        }
    }
}
#include <initializer_list>
bool miller_rabin(long long n) {
    if (n == 1) return 0;
    long long d = n - 1, s = 0;
    while (~d & 1) d >>= 1, s++;
    auto check = [&](long long a) -> bool {
        long long x = modpow(a, d, n);
        if (x == 1) return 1;
        long long y = n - 1;
        for (int i = 0; i < s; i++) {
            if (x == y) return true;
            x = modmul(x, x, n);
        }
        return false;
    };
    for (long long a : {2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37}) {
        if (a >= n) break;
        if (!check(a)) return false;
    }
    return true;
}
#line 59 "/Users/gyouzasushi/kyopro/library/math/factorize.hpp"
std::map<long long, int> factorize(long long n) {
    std::map<long long, int> ret;
    while (~n & 1) n >>= 1, ret[2]++;
    std::queue<long long> q;
    q.push(n);
    while (!q.empty()) {
        long long p = q.front();
        q.pop();
        if (p == 1) continue;
        if (miller_rabin(p)) {
            ret[p]++;
            continue;
        }
        long long d = rho(p);
        q.push(d);
        q.push(p / d);
    }
    return ret;
}
#line 49 "/Users/gyouzasushi/kyopro/library/math/binomial_coefficient.hpp"
struct binomial_coefficient_arbitrary_mod {
    static void set_mod(int mod) {
        assert(1 <= mod);
        m = mod;
        factors = factorize(m);
        f.assign(factors.size(), {});
        inv_f.assign(factors.size(), {});
    }
    static long long C(long long n, long long k) {
        if (m == 1 || n < 0 || n < k || k < 0) return 0;
        ensure(n);
        long long r = n - k;
        std::vector<long long> rems(factors.size()), mods(factors.size());
        int id = 0;
        for (auto [p, q] : factors) {
            long long p_q = pow_ll(p, q);
            mods[id] = p_q;
            long long e1 = 0, e2 = 0;
            for (long long p_i = p_q;;) {
                e1 += n / p_i - k / p_i - r / p_i;
                if (p_i > n / p) break;
                p_i *= p;
            }
            for (long long p_i = p;;) {
                e2 += n / p_i - k / p_i - r / p_i;
                if (p_i > n / p) break;
                p_i *= p;
            }
            atcoder::internal::barrett bt((unsigned int)(p_q));
            long long delta = p == 2 && q >= 3 ? 1 : -1;
            long long rem = delta == -1 && e1 & 1 ? p_q - 1 : 1;
            rem = bt.mul(rem, atcoder::pow_mod(p, e2, p_q));
            for (long long p_i = 1;;) {
                rem = bt.mul(rem, f[id][(n / p_i) % p_q]);
                rem = bt.mul(rem, inv_f[id][(k / p_i) % p_q]);
                rem = bt.mul(rem, inv_f[id][(r / p_i) % p_q]);
                if (p_i > n / p) break;
                p_i *= p;
            }
            rems[id] = rem;
            id++;
        }
        return atcoder::crt(rems, mods).first;
    }

private:
    static void ensure(long long n) {
        if (max_size > n) return;
        int id = 0;
        for (auto [p, q] : factors) {
            long long p_q = pow_ll(p, q);
            int sz = f[id].size();
            if ((long long)sz > std::min(p_q - 1, n) + 1) continue;
            f[id].resize(std::min(p_q - 1, n) + 1);
            inv_f[id].resize(std::min(p_q - 1, n) + 1);
            max_size = std::max(max_size, std::min(p_q - 1, n) + 1);
            atcoder::internal::barrett bt((unsigned int)(p_q));
            for (int i = sz; i <= std::min(p_q - 1, n); i++) {
                if (i == 0) {
                    f[id][i] = 1;
                } else {
                    if (i % p == 0) {
                        f[id][i] = f[id][i - 1];
                    } else {
                        f[id][i] = bt.mul(f[id][i - 1], i);
                    }
                }
                inv_f[id][i] = atcoder::inv_mod(f[id][i], p_q);
            }
            id++;
        }
    }
    static long long pow_ll(long long x, long long n) {
        assert(0 <= n && 1 <= m);
        long long r = 1, y = x;
        while (n) {
            if (n & 1) r *= y;
            n >>= 1;
            if (n) y *= y;
        }
        return r;
    }
    static inline long long m = -1;
    static inline long long max_size = 0;
    static inline std::map<long long, int> factors{};
    static inline std::vector<std::vector<long long>> f{};
    static inline std::vector<std::vector<long long>> inv_f{};
};
#line 74 "main.cpp"
using binom = binomial_coefficient<mint>;
using fact = factorial_table<mint>;
int main() {
    ll n, p;
    cin >> n >> p;
    mint ans = fact::val(n) - 1;
    mint x = 1;
    for (ll d = 1; d * p <= n; d++) {
        x *= binom::C(n - (d - 1) * p, p) * fact::val(p - 1);
        ans -= x * fact::inv(d);
    }
    cout << ans.val() << '\n';
}