#line 1 "playspace/main.cpp"
#include <bits/stdc++.h>
#line 4 "library/gandalfr/math/Eratosthenes.hpp"

#line 6 "library/gandalfr/math/Eratosthenes.hpp"

#line 6 "library/gandalfr/math/enumeration_utility.hpp"

#line 1 "library/atcoder/modint.hpp"



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

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

#line 1 "library/atcoder/internal_math.hpp"



#line 5 "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 "library/atcoder/internal_type_traits.hpp"



#line 7 "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 "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 4 "library/gandalfr/math/formal_power_series.hpp"

#line 1 "library/atcoder/convolution.hpp"



#line 9 "library/atcoder/convolution.hpp"

#line 1 "library/atcoder/internal_bit.hpp"



#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`
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


#line 12 "library/atcoder/convolution.hpp"

namespace atcoder {

namespace internal {

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

    static bool first = true;
    static mint sum_e[30];  // sum_e[i] = ies[0] * ... * ies[i - 1] * es[i]
    if (first) {
        first = false;
        mint es[30], ies[30];  // es[i]^(2^(2+i)) == 1
        int cnt2 = bsf(mint::mod() - 1);
        mint e = mint(g).pow((mint::mod() - 1) >> cnt2), ie = e.inv();
        for (int i = cnt2; i >= 2; i--) {
            // e^(2^i) == 1
            es[i - 2] = e;
            ies[i - 2] = ie;
            e *= e;
            ie *= ie;
        }
        mint now = 1;
        for (int i = 0; i <= cnt2 - 2; i++) {
            sum_e[i] = es[i] * now;
            now *= ies[i];
        }
    }
    for (int ph = 1; ph <= h; ph++) {
        int w = 1 << (ph - 1), p = 1 << (h - ph);
        mint now = 1;
        for (int s = 0; s < w; s++) {
            int offset = s << (h - ph + 1);
            for (int i = 0; i < p; i++) {
                auto l = a[i + offset];
                auto r = a[i + offset + p] * now;
                a[i + offset] = l + r;
                a[i + offset + p] = l - r;
            }
            now *= sum_e[bsf(~(unsigned int)(s))];
        }
    }
}

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

    static bool first = true;
    static mint sum_ie[30];  // sum_ie[i] = es[0] * ... * es[i - 1] * ies[i]
    if (first) {
        first = false;
        mint es[30], ies[30];  // es[i]^(2^(2+i)) == 1
        int cnt2 = bsf(mint::mod() - 1);
        mint e = mint(g).pow((mint::mod() - 1) >> cnt2), ie = e.inv();
        for (int i = cnt2; i >= 2; i--) {
            // e^(2^i) == 1
            es[i - 2] = e;
            ies[i - 2] = ie;
            e *= e;
            ie *= ie;
        }
        mint now = 1;
        for (int i = 0; i <= cnt2 - 2; i++) {
            sum_ie[i] = ies[i] * now;
            now *= es[i];
        }
    }

    for (int ph = h; ph >= 1; ph--) {
        int w = 1 << (ph - 1), p = 1 << (h - ph);
        mint inow = 1;
        for (int s = 0; s < w; s++) {
            int offset = s << (h - ph + 1);
            for (int i = 0; i < p; i++) {
                auto l = a[i + offset];
                auto r = a[i + offset + p];
                a[i + offset] = l + r;
                a[i + offset + p] =
                    (unsigned long long)(mint::mod() + l.val() - r.val()) *
                    inow.val();
            }
            inow *= sum_ie[bsf(~(unsigned int)(s))];
        }
    }
}

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

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

}  // namespace internal

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

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

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

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

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

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

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

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

    std::vector<long long> c(n + m - 1);
    for (int i = 0; i < n + m - 1; i++) {
        unsigned long long x = 0;
        x += (c1[i] * i1) % MOD1 * M2M3;
        x += (c2[i] * i2) % MOD2 * M1M3;
        x += (c3[i] * i3) % MOD3 * M1M2;
        // B = 2^63, -B <= x, r(real value) < B
        // (x, x - M, x - 2M, or x - 3M) = r (mod 2B)
        // r = c1[i] (mod MOD1)
        // focus on MOD1
        // r = x, x - M', x - 2M', x - 3M' (M' = M % 2^64) (mod 2B)
        // r = x,
        //     x - M' + (0 or 2B),
        //     x - 2M' + (0, 2B or 4B),
        //     x - 3M' + (0, 2B, 4B or 6B) (without mod!)
        // (r - x) = 0, (0)
        //           - M' + (0 or 2B), (1)
        //           -2M' + (0 or 2B or 4B), (2)
        //           -3M' + (0 or 2B or 4B or 6B) (3) (mod MOD1)
        // we checked that
        //   ((1) mod MOD1) mod 5 = 2
        //   ((2) mod MOD1) mod 5 = 3
        //   ((3) mod MOD1) mod 5 = 4
        long long diff =
            c1[i] - internal::safe_mod((long long)(x), (long long)(MOD1));
        if (diff < 0) diff += MOD1;
        static constexpr unsigned long long offset[5] = {
            0, 0, M1M2M3, 2 * M1M2M3, 3 * M1M2M3};
        x -= offset[diff % 5];
        c[i] = x;
    }

    return c;
}

}  // namespace atcoder


#line 7 "library/gandalfr/math/formal_power_series.hpp"

// https://web.archive.org/web/20220813112322/https://opt-cp.com/fps-implementation/#toc2
template<class T> struct FormalPowerSeries : public std::vector<T> {
    using std::vector<T>::vector;
    using std::vector<T>::operator=;
    using F = FormalPowerSeries;

    F operator-() const {
        F res(*this);
        for (auto &e : res) e = -e;
        return res;
    }
    F &operator*=(const T &g) {
        for (auto &e : *this) e *= g;
        return *this;
    }
    F &operator/=(const T &g) {
        assert(g != T(0));
        *this *= g.inv();
        return *this;
    }
    F &operator+=(const F &g) {
        int n = (*this).size(), m = g.size();
        for(int i = 0; i < std::min(n, m); ++i) (*this)[i] += g[i];
        return *this;
    }
    F &operator-=(const F &g) {
        int n = (*this).size(), m = g.size();
        for(int i = 0; i < std::min(n, m); ++i) (*this)[i] -= g[i];
        return *this;
    }
    F &operator<<=(const int d) {
        int n = (*this).size();
        (*this).insert((*this).begin(), d, 0);
        (*this).resize(n);
        return *this;
    }
    F &operator>>=(const int d) {
        int n = (*this).size();
        (*this).erase((*this).begin(), (*this).begin() + std::min(n, d));
        (*this).resize(n);
        return *this;
    }
    F inv(int d = -1) const {
        int n = (*this).size();
        assert(n != 0 && (*this)[0] != 0);
        if (d == -1) d = n;
        assert(d > 0);
        F res{(*this)[0].inv()};
        while ((int)res.size() < d) {
        int m = size(res);
        F f(begin(*this), begin(*this) + std::min(n, 2*m));
        F r(res);
        f.resize(2*m), atcoder::internal::butterfly(f);
        r.resize(2*m), atcoder::internal::butterfly(r);
        for(int i = 0; i < 2 * m; ++i) f[i] *= r[i];
        atcoder::internal::butterfly_inv(f);
        f.erase(f.begin(), f.begin() + m);
        f.resize(2*m), atcoder::internal::butterfly(f);
        for(int i = 0; i < 2 * m; ++i) f[i] *= r[i];
        atcoder::internal::butterfly_inv(f);
        T iz = T(2*m).inv(); iz *= -iz;
        for(int i = 0; i < m; ++i) f[i] *= iz;
        res.insert(res.end(), f.begin(), f.begin() + m);
        }
        return {res.begin(), res.begin() + d};
    }

    // fast: FMT-friendly modulus only
    F &operator*=(const F &g) {
        int n = (*this).size();
        *this = convolution(*this, g);
        (*this).resize(n);
        return *this;
    }
    F &operator/=(const F &g) {
        int n = (*this).size();
        *this = convolution(*this, g.inv(n));
        (*this).resize(n);
        return *this;
    }

    // naive
    F &naive_mult(const F &g) {
        int n = (*this).size(), m = g.size();
        for(int i = n - 1; i >= 0; --i) {
        (*this)[i] *= g[0];
        for(int j = 1; j < std::min(i+1, m); ++j) (*this)[i] += (*this)[i-j] * g[j];
        }
        return *this;
    }
    F &naive_div(const F &g) {
        assert(g[0] != T(0));
        T ig0 = g[0].inv();
        int n = (*this).size(), m = g.size();
        for(int i = 0; i < n; ++i) {
        for(int j = 1; j < std::min(i+1, m); ++j) (*this)[i] -= (*this)[i-j] * g[j];
        (*this)[i] *= ig0;
        }
        return *this;
    }

    // sparse
    F &sparse_mult(const std::vector<std::pair<int, T>> &g) {
        int n = (*this).size();
        auto [d, c] = g.front();
        if (d == 0) g.erase(g.begin());
        else c = 0;
        for(int i = n - 1; i >= 0; --i) {
        (*this)[i] *= c;
        for (auto &[j, b] : g) {
            if (j > i) break;
            (*this)[i] += (*this)[i-j] * b;
        }
        }
        return *this;
    }
    F &sparse_div(const std::vector<std::pair<int, T>> &g) {
        int n = (*this).size();
        auto [d, c] = g.front();
        assert(d == 0 && c != T(0));
        T ic = c.inv();
        g.erase(g.begin());
        for(int i = 0; i < n; ++i) {
        for (auto &[j, b] : g) {
            if (j > i) break;
            (*this)[i] -= (*this)[i-j] * b;
        }
        (*this)[i] *= ic;
        }
        return *this;
    }

    F &operator^=(long long n) {
        if (n == 0) {
            std::fill(this->begin(), this->end(), T(0));
            (*this)[0] = 1;
            return *this;
        }
        F f(*this);
        --n;
        while (n > 0) {
            if (n & 1)
                *this *= f;
            f = f * f;
            n >>= 1;
        }
        return *this;
    }

    // multiply and divide (1 + cz^d)
    void multiply(const int d, const T c) { 
        int n = (*this).size();
        if (c == T(1)) for(int i = n - d - 1; i >= 0; --i) (*this)[i+d] += (*this)[i];
        else if (c == T(-1)) for(int i = n - d - 1; i >= 0; --i) (*this)[i+d] -= (*this)[i];
        else for(int i = n - d - 1; i >= 0; --i) (*this)[i+d] += (*this)[i] * c;
    }
    void divide(const int d, const T c) {
        int n = (*this).size();
        if (c == T(1)) for(int i = 0; i < n - d; ++i) (*this)[i+d] -= (*this)[i];
        else if (c == T(-1)) for(int i = 0; i < n - d; ++i) (*this)[i+d] += (*this)[i];
        else for(int i = 0; i < n - d; ++i) (*this)[i+d] -= (*this)[i] * c;
    }

    T eval(const T &a) const {
        T x(1), res(0);
        for (auto e : *this) res += e * x, x *= a;
        return res;
    }

    friend F operator*(const T &g, const F &f) { return F(f) *= g; }
    friend F operator/(const T &g, const F &f) { return F(f) /= g; }
    friend F operator+(const F &f1, const F &f2) { return F(f1) += f2; }
    friend F operator-(const F &f1, const F &f2) { return F(f1) -= f2; }
    friend F operator<<(const F &f, const int d) { return F(f) <<= d; }
    friend F operator>>(const F &f, const int d) { return F(f) >>= d; }
    friend F operator*(const F &f1, const F &f2) { return F(f1) *= f2; }
    friend F operator/(const F &f1, const F &f2) { return F(f1) /= f2; }
    friend F operator*(const F &f, const std::vector<std::pair<int, T>> &g) { return F(f) *= g; }
    friend F operator/(const F &f, const std::vector<std::pair<int, T>> &g) { return F(f) /= g; }
    friend F operator^(const F &f, long long g) { return F(f) ^= g; }

};
#line 9 "library/gandalfr/math/enumeration_utility.hpp"

template <class T> T power(T x, long long n) {
    T ret = static_cast<T>(1);
    while (n > 0) {
        if (n & 1)
            ret = ret * x;
        x = x * x;
        n >>= 1;
    }
    return ret;
}

long long power(long long x, long long n) {
    long long ret = 1;
    while (n > 0) {
        if (n & 1)
            ret = ret * x;
        x = x * x;
        n >>= 1;
    }
    return ret;
}

long long power(long long x, long long n, int MOD) {
    long long ret = 1;
    x %= MOD;
    while (n > 0) {
        if (n & 1)
            ret = ret * x % MOD;
        x = x * x % MOD;
        n >>= 1;
    }
    return ret;
}

long long power(long long x, long long n, long long MOD) {
    long long ret = 1;
    x %= MOD;
    while (n > 0) {
        if (n & 1)
            ret = (__int128_t)ret * x % MOD;
        x = (__int128_t)x * x % MOD;
        n >>= 1;
    }
    return ret;
}

template <int m> class factorial {
  private:
    static inline std::vector<atcoder::static_modint<m>> fact{1};

  public:
    factorial() = delete;
    ~factorial() = delete;
    static atcoder::static_modint<m> get(int n) {
        while (n >= (int)fact.size())
            fact.push_back(fact.back() * fact.size());
        return fact[n];
    }
};
atcoder::modint1000000007 (*fact1000000007)(int) = factorial<1000000007>::get;
atcoder::modint998244353 (*fact998244353)(int) = factorial<998244353>::get;

template <int m> static atcoder::static_modint<m> permutation(int n, int k) {
    assert(0 <= k && k <= n);
    return factorial<m>::get(n) / factorial<m>::get(n - k);
}
atcoder::modint1000000007 (*perm1000000007)(int, int) = permutation<1000000007>;
atcoder::modint998244353 (*perm998244353)(int, int) = permutation<998244353>;

template <int m> static atcoder::static_modint<m> combnation(int n, int k) {
    assert(0 <= k && k <= n);
    return factorial<m>::get(n) /
           (factorial<m>::get(k) * factorial<m>::get(n - k));
}
atcoder::modint1000000007 (*comb1000000007)(int, int) = combnation<1000000007>;
atcoder::modint998244353 (*comb998244353)(int, int) = combnation<998244353>;

template <int m> static FormalPowerSeries<atcoder::static_modint<m>> Bernoulli_number(int n) {
    assert(0 <= n);
    FormalPowerSeries<atcoder::static_modint<m>> F(n, 0);
    F[0] = 1;
    for (int i = 1; i < n; ++i) {
        F[i] = F[i - 1] / (i + 1);
    }
    F = F.inv();
    for (int i = 0; i < n; ++i) {
        F[i] *= factorial<m>::get(i);
    }
    return F;
}
FormalPowerSeries<atcoder::modint998244353> (*Bernoulli998244353)(int) = Bernoulli_number<998244353>;
#line 8 "library/gandalfr/math/Eratosthenes.hpp"

/**
 * @see https://drken1215.hatenablog.com/entry/2023/05/23/233000
 */
bool MillerRabin(long long N, const std::vector<long long> &A) {
    long long s = 0, d = N - 1;
    while (d % 2 == 0) {
        ++s;
        d >>= 1;
    }
    for (auto a : A) {
        if (N <= a)
            return true;
        long long t, x = power(a, d, N);
        if (x != 1) {
            for (t = 0; t < s; ++t) {
                if (x == N - 1)
                    break;
                x = (__int128_t)x * x % N;
            }
            if (t == s)
                return false;
        }
    }
    return true;
}

/**
 * @brief 素数判定や列挙をサポートするクラス
 * @brief 素数篩を固定サイズで構築、それをもとに素数列挙などを行う
 * @attention 構築サイズが (2^23) でおよそ 0.5s
 */
class Eratosthenes {
  protected:
    static inline int seive_size = (1 << 23);
    static inline std::vector<bool> sieve;
    static inline std::vector<int> primes{2, 3}, movius, min_factor;

    static void make_table() {
        sieve.assign(seive_size, true);
        sieve[0] = sieve[1] = false;
        movius.assign(seive_size, 1);
        min_factor.assign(seive_size, 1);
        for (int i = 2; i <= seive_size; ++i) {
            if (!sieve[i])
                continue;
            movius[i] = -1;
            min_factor[i] = i;
            primes.push_back(i);
            for (int j = i * 2; j < seive_size; j += i) {
                sieve[j] = false;
                movius[j] = ((j / i) % i == 0 ? 0 : -movius[j]);
                if (min_factor[j] == 1)
                    min_factor[j] = i;
            }
        }
    }

    static std::vector<std::pair<long long, int>> fast_factorize(long long n) {
        std::vector<std::pair<long long, int>> ret;
        while (n > 1) {
            if (ret.empty() || ret.back().first != min_factor[n]) {
                ret.push_back({min_factor[n], 1});
            } else {
                ret.back().second++;
            }
            n /= min_factor[n];
        }
        return ret;
    }

    static std::vector<std::pair<long long, int>> naive_factorize(long long n) {
        std::vector<std::pair<long long, int>> ret;
        for (long long p : primes) {
            if (n == 1 || p * p > n)
                break;
            while (n % p == 0) {
                if (ret.empty() || ret.back().first != p)
                    ret.push_back({p, 1});
                else
                    ret.back().second++;
                n /= p;
            }
        }
        if (n != 1)
            ret.push_back({n, 1});
        return ret;
    }

  public:
    Eratosthenes() = delete;
    ~Eratosthenes() = delete;

    static void set_sieve_size(int size) {
        assert(sieve.empty());
        seive_size = size;
    }

    /**
     * @brief n が素数かを判定
     */
    static bool is_prime(long long n) {
        if (sieve.empty())
            make_table();
        assert(1 <= n);

        if (n > 2 && (n & 1LL) == 0) {
            return false;
        } else if (n < seive_size) {
            return sieve[n];
        } else if (n < 4759123141LL) {
            return MillerRabin(n, {2, 7, 61});
        } else {
            return MillerRabin(
                n, {2, 325, 9375, 28178, 450775, 9780504, 1795265022});
        }
    }

    /**
     * @brief 素因数分解する
     * @return factorize(p1^e1 * p2^e2 * ...) => {{p1, e1}, {p2, e2], ...},
     * @return factorize(1) => {}
     */
    static std::vector<std::pair<long long, int>> factorize(long long n) {
        if (sieve.empty())
            make_table();
        assert(1 <= n);

        if (n < seive_size) {
            return fast_factorize(n);
        } else {
            return naive_factorize(n);
        }
    }

    static int Movius(int n) {
        if (movius.empty())
            make_table();
        assert(1 <= n);
        return movius.at(n);
    }

    /**
     * @brief 約数列挙
     * @attention if n < sieve_size : O(N^(1/loglogN))
     */
    template <bool sort = true>
    static std::vector<long long> divisors(long long n) {
        std::vector<long long> ds;
        auto facs(factorize(n));
        auto rec = [&](auto self, long long d, int cu) -> void {
            if (cu == (int)facs.size()) {
                ds.push_back(d);
                return;
            }
            for (int e = 0; e <= facs[cu].second; ++e) {
                self(self, d, cu + 1);
                d *= facs[cu].first;
            }
        };
        rec(rec, 1LL, 0);
        if constexpr (sort)
            std::sort(ds.begin(), ds.end());
        return ds;
        ;
    }

    /**
     * @brief オイラーのトーシェント関数
     */
    static long long totient(long long n) {
        long long ret = 1;
        for (auto [b, e] : factorize(n))
            ret *= power(b, e - 1) * (b - 1);
        return ret;
    }

    static int kth_prime(int k) { return primes.at(k); }
};
#line 8 "library/gandalfr/other/io_supporter.hpp"

#line 10 "library/gandalfr/other/io_supporter.hpp"

template <typename T>
std::ostream &operator<<(std::ostream &os, const std::vector<T> &v) {
    for (int i = 0; i < (int)v.size(); i++)
        os << v[i] << (i + 1 != (int)v.size() ? " " : "");
    return os;
}
template <typename T>
std::ostream &operator<<(std::ostream &os, const std::set<T> &st) {
    for (const T &x : st) {
        std::cout << x << " ";
    }
    return os;
}

template <typename T>
std::ostream &operator<<(std::ostream &os, const std::multiset<T> &st) {
    for (const T &x : st) {
        std::cout << x << " ";
    }
    return os;
}
template <typename T>
std::ostream &operator<<(std::ostream &os, const std::deque<T> &dq) {
    for (const T &x : dq) {
        std::cout << x << " ";
    }
    return os;
}
template <typename T1, typename T2>
std::ostream &operator<<(std::ostream &os, const std::pair<T1, T2> &p) {
    os << p.first << ' ' << p.second;
    return os;
}
template <typename T>
std::ostream &operator<<(std::ostream &os, std::queue<T> &q) {
    int sz = q.size();
    while (--sz) {
        os << q.front() << ' ';
        q.push(q.front());
        q.pop();
    }
    os << q.front();
    q.push(q.front());
    q.pop();
    return os;
}

namespace atcoder {
template <int m>
std::ostream &operator<<(std::ostream &os, const static_modint<m> &mi) {
    os << mi.val();
    return os;
}
template <int m>
std::ostream &operator<<(std::ostream &os, const dynamic_modint<m> &mi) {
    os << mi.val();
    return os;
}

}

template <typename T>
std::istream &operator>>(std::istream &is, std::vector<T> &v) {
    for (T &in : v)
        is >> in;
    return is;
}
template <typename T1, typename T2>
std::istream &operator>>(std::istream &is, std::pair<T1, T2> &p) {
    is >> p.first >> p.second;
    return is;
}
namespace atcoder {
template <int m>
std::istream &operator>>(std::istream &is, static_modint<m> &mi) {
    long long n;
    is >> n;
    mi = n;
    return is;
}
template <int m>
std::istream &operator>>(std::istream &is, dynamic_modint<m> &mi) {
    long long n;
    is >> n;
    mi = n;
    return is;
}

}
#line 5 "playspace/main.cpp"
using namespace std;
using ll = long long;
const int INF = 1001001001;
const ll INFLL = 1001001001001001001;
const ll MOD  = 1000000007;
const ll _MOD = 998244353;
#define rep(i, j, n) for(ll i = (ll)(j); i < (ll)(n); i++)
#define rrep(i, j, n) for(ll i = (ll)(n-1); i >= (ll)(j); i--)
#define all(a) (a).begin(),(a).end()
#define debug(a) std::cerr << #a << ": " << a << std::endl
#define LF cout << endl
template<typename T1, typename T2> inline bool chmax(T1 &a, T2 b) { return a < b && (a = b, true); }
template<typename T1, typename T2> inline bool chmin(T1 &a, T2 b) { return a > b && (a = b, true); }
void Yes(bool ok){ std::cout << (ok ? "Yes" : "No") << std::endl; }

int main(void){

    ll H, W, K;
    cin >> H >> W >> K;
    atcoder::modint998244353 ans = 0;
    for (auto h: Eratosthenes::divisors(K)) {
        auto w = K / h;
        if (h <= H && w <= W) {
            ans += comb998244353(H, h) * comb998244353(W, w);
        }
    }
    cout << ans << endl;



}