結果

問題 No.2527 H and W
ユーザー 👑 seekworserseekworser
提出日時 2023-02-28 21:37:28
言語 C++23
(gcc 12.3.0 + boost 1.83.0)
結果
AC  
実行時間 107 ms / 2,000 ms
コード長 29,330 bytes
コンパイル時間 3,319 ms
コンパイル使用メモリ 261,740 KB
実行使用メモリ 26,772 KB
最終ジャッジ日時 2024-09-23 07:24:15
合計ジャッジ時間 6,898 ms
ジャッジサーバーID
(参考情報)
judge2 / judge3
このコードへのチャレンジ
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テストケース

テストケース表示
入力 結果 実行時間
実行使用メモリ
testcase_00 AC 95 ms
26,632 KB
testcase_01 AC 91 ms
26,676 KB
testcase_02 AC 93 ms
26,512 KB
testcase_03 AC 92 ms
26,736 KB
testcase_04 AC 102 ms
26,688 KB
testcase_05 AC 107 ms
26,720 KB
testcase_06 AC 104 ms
26,604 KB
testcase_07 AC 95 ms
26,508 KB
testcase_08 AC 89 ms
26,688 KB
testcase_09 AC 93 ms
26,732 KB
testcase_10 AC 91 ms
26,580 KB
testcase_11 AC 101 ms
26,740 KB
testcase_12 AC 100 ms
26,644 KB
testcase_13 AC 94 ms
26,732 KB
testcase_14 AC 87 ms
26,576 KB
testcase_15 AC 99 ms
26,572 KB
testcase_16 AC 94 ms
26,772 KB
testcase_17 AC 89 ms
26,648 KB
testcase_18 AC 89 ms
26,612 KB
testcase_19 AC 93 ms
26,692 KB
testcase_20 AC 91 ms
26,504 KB
testcase_21 AC 90 ms
26,672 KB
testcase_22 AC 93 ms
26,528 KB
testcase_23 AC 90 ms
26,680 KB
testcase_24 AC 90 ms
26,616 KB
testcase_25 AC 88 ms
26,600 KB
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ソースコード

diff #

#line 2 "/home/seekworser/.cpp_lib/competitive_library/competitive/std/std.hpp"
#include <bits/stdc++.h>
#ifndef LOCAL_TEST
#pragma GCC target ("avx")
#pragma GCC optimize("O3")
#pragma GCC optimize("unroll-loops")
#pragma GCC target("sse,sse2,sse3,ssse3,sse4,popcnt,abm,mmx,avx,tune=native")
#endif // LOCAL_TEST
using namespace std;
// 型名の短縮
using ll = long long;
using pii = pair<int, int>; using pll = pair<ll, ll>;
using vi = vector<int>;  using vvi = vector<vi>; using vvvi = vector<vvi>;
using vl = vector<ll>;  using vvl = vector<vl>; using vvvl = vector<vvl>;
using vb = vector<bool>; using vvb = vector<vb>; using vvvb = vector<vvb>;
using vc = vector<char>; using vvc = vector<vc>; using vvvc = vector<vvc>;
using vd = vector<double>; using vvd = vector<vd>; using vvvd = vector<vvd>;
using vs = vector<string>; using vvs = vector<vector<string>>; using vvvs = vector<vector<vector<string>>>;
template <class T> using priority_queue_min = priority_queue<T, vector<T>, greater<T>>;
// 定数の定義
constexpr double PI = 3.14159265358979323;
constexpr int INF = 100100111; constexpr ll INFL = 3300300300300300491LL;
float EPS = 1e-8; double EPSL = 1e-16;
bool eq(const double x, const double y) { return abs(x - y) < EPSL; }
bool eq(const float x, const float y) { return abs(x - y) < EPS; }
template<typename T> bool eq(const T x, const T y) { return x == y; }
template<typename T> bool neq(const T x, const T y) { return !(eq(x, y)); }
template<typename T> bool ge(const T x, const T y) { return eq(x, y) || (x > y); }
template<typename T> bool le(const T x, const T y) { return eq(x, y) || (x < y); }
template<typename T> bool gt(const T x, const T y) { return !(le(x, y)); }
template<typename T> bool lt(const T x, const T y) { return !(ge(x, y)); }
constexpr int MODINT998244353 = 998244353;
constexpr int MODINT1000000007 = 1000000007;
// 入出力高速化
struct Nyan { Nyan() { cin.tie(nullptr); ios::sync_with_stdio(false); cout << fixed << setprecision(18); } } nyan;
// 汎用マクロの定義
#define all(a) (a).begin(), (a).end()
#define sz(x) ((int)(x).size())
#define rep(i, n) for(ll i = 0, i##_len = ll(n); i < i##_len; ++i) // 0 から n-1 まで昇順
#define repi(i, s, t) for(ll i = ll(s), i##_end = ll(t); i < i##_end; ++i) // s から t まで昇順
#define repis(i, s, t, step) for(ll i = ll(s), i##_end = ll(t); i < i##_end; i+=step) // s から t まで stepずつ
#define repir(i, s, t, step) for(ll i = ll(s), i##_end = ll(t); i > i##_end; i+=step) // s から t まで stepずつ
#define repe(a, v) for(auto& a : (v)) // v の全要素(変更可能)
#define smod(n, m) ((((n) % (m)) + (m)) % (m)) // 非負mod
#define sdiv(n, m) (((n) - smod(n, m)) / (m)) // 非負div
#define uniq(a) {sort(all(a)); (a).erase(unique(all(a)), (a).end());} // 重複除去
void Yes(bool b) { cout << (b ? "Yes\n" : "No\n"); return; };
void YES(bool b) { cout << (b ? "YES\n" : "NO\n"); return; };
template<typename T, size_t N> T max(array<T, N>& a) { return *max_element(all(a)); };
template<typename T, size_t N> T min(array<T, N>& a) { return *min_element(all(a)); };
template<typename T> T max(vector<T>& a) { return *max_element(all(a)); };
template<typename T> T min(vector<T>& a) { return *min_element(all(a)); };
template<typename T> T sum(vector<T>& a, T zero = T(0)) { T rev = zero; rep(i, sz(a)) rev += a[i]; return rev; };

// modでのpow
ll powm(ll a, ll n, ll mod=INFL) {
    ll res = 1;
    while (n > 0) {
        if (n & 1) res = (res * a) % mod;
        if (n > 1) a = (a * a) % mod;
        n >>= 1;
    }
    return res;
}
// 整数Sqrt
ll sqrtll(ll x) {
    assert(x >= 0);
    ll hi(x), lo(0);
    while (hi != lo) {
        ll y = (hi + lo + 1) / 2;
        if (y <= x/y) lo = y;
        else hi = y - 1;
    }
    return lo;
}
template <class T> inline bool chmax(T& M, const T& x) { if (M < x) { M = x; return true; } return false; } // 最大値を更新(更新されたら true を返す)
template <class T> inline bool chmin(T& m, const T& x) { if (m > x) { m = x; return true; } return false; } // 最小値を更新(更新されたら true を返す)
int digit(ll x, int d=10) { int rev=0; while (x > 0) { rev++; x /= d;}; return rev; } // xのd進数桁数
/**
 * @brief std.hpp
 * @docs docs/std/std.md
 */
#line 3 "/home/seekworser/.cpp_lib/competitive_library/competitive/math/prime.hpp"
template <class T> bool is_prime(T n) {
    if (n == 1) return false;
    for (T i=2; i <= (T)std::sqrt(n); i++) {
        if (n % i == 0) return false;
    }
    return true;
};
//return all devisor
template <class T> vector<T> divisor(T n, bool sorted=true) {
    vector<T> ans(0);
    for (T i = 1; i <= (T)std::sqrt(n); i++) {
        if (n % i == 0) {
            ans.push_back(i);
            if (i * i != n) ans.push_back(n / i);
        }
    }
    if (sorted) sort(ans.begin(), ans.end());
    return ans;
};
template <class T> vector<T> prime_factor(T n) {
    vector<T> ans(0);
    for (T i = 2; i <= (T)std::sqrt(n); i++) {
        while (n % i == 0) {
            ans.push_back(i);
            n /= i;
        }
    }
    if (n != 1) ans.push_back(n);
    return ans;
};
template <class T> map<T, T> prime_factor_c(T n) {
    map<T, T> ans;
    for (T i = 2; i <= (T)std::sqrt(n); i++) {
        while (n % i == 0) {
            ans[i] += 1;
            n /= i;
        }
    }
    if (n != 1) ans[n] += 1;
    return ans;
};
template <class T> vector<T> primes(T n) {
    vector<T> ans(0);
    if (n < 2) return ans;
    vector<bool> is_primev(n+1, true);
    is_primev.at(0) = is_primev.at(1) = false;
    for (T i = 2; i <= (T)std::sqrt(n); i++) {
        if (!is_primev.at(i)) continue;
        for (T j = i*2; j <= n; j+=i) is_primev.at(j) = false;
    }
    for (T i = 2; i <= n; i++) {
        if (is_primev.at(i)) ans.push_back(i);
    }
    return ans;
};
template <class T> vector<T> segment_seive(T s, T t) {
    vector<T> ans(0);
    if (t < 2 || s < 0 || s >= t) return ans;
    vector<bool> is_prime_small((T)std::sqrt(t)+1, true);
    vector<bool> is_prime_large(t-s, true);
    for (T i = 2; i <= (T)std::sqrt(t); i++) {
        if (!is_prime_small.at(i)) continue;
        for (T j = i*2; j*j < t; j+=i) is_prime_small.at(j) = false;
        for (T j = max(2*i, ((s+i-1)/i)*i); j < t; j+=i) is_prime_large.at(j-s) = false;
    }
    for (T i=0; i < t-s; i++) {
        if (is_prime_large.at(i) && s+i != 1) ans.push_back(s+i);
    }
    return ans;
};
/**
 * @brief prime.hpp
 * @docs docs/math/prime.md
 */
#line 3 "/home/seekworser/.cpp_lib/competitive_library/competitive/math/combination.hpp"
struct Combination {
    ll pm;
    vl fact, fact_inv;
    Combination(int n = 1000003, ll p = 998244353) : fact(n), fact_inv(n){
        vl inv(n);
        pm = p;
        fact[0] = fact[1] = 1;
        fact_inv[0] = fact_inv[1] = 1;
        inv[0] = 0;
        inv[1] = 1;
        for (int i = 2; i < n; i++) {
            fact[i] = fact[i - 1] * i % p;
            inv[i] = p - inv[p % i] * (p / i) % p;
            fact_inv[i] = fact_inv[i - 1] * inv[i] % p;
        }
    }
    ll operator()(int n, int r) {
        if (r < 0 || n < r) return 0;
        return fact[n] * (fact_inv[r] * fact_inv[n - r] % pm) % pm;
    }
};
/**
 * @brief combination.hpp
 * @docs docs/math/combination.md
 */
#line 4 "/home/seekworser/.cpp_lib/competitive_library/atcoder/modint.hpp"
#include <type_traits>

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

#line 3 "/home/seekworser/.cpp_lib/competitive_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 5 "/home/seekworser/.cpp_lib/competitive_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 12 "/home/seekworser/.cpp_lib/competitive_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 mint& rhs) { (*this)._v = rhs.val(); return *this; }

    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 mint& rhs) { (*this)._v = rhs.val(); return *this; }

    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 "/home/seekworser/.cpp_lib/competitive_library/competitive/math/modint.hpp"
inline std::istream& operator>>(std::istream& is, atcoder::modint& x);
inline std::istream& operator>>(std::istream& is, atcoder::modint998244353& x);
inline std::istream& operator>>(std::istream& is, atcoder::modint1000000007& x);
inline std::ostream& operator<<(std::ostream& os, const atcoder::modint& x);
inline std::ostream& operator<<(std::ostream& os, const atcoder::modint998244353& x);
inline std::ostream& operator<<(std::ostream& os, const atcoder::modint1000000007& x);
inline std::istream& operator>>(std::istream& is, atcoder::modint& x) {ll a; is >> a; x = a; return is; }
inline std::istream& operator>>(std::istream& is, atcoder::modint998244353& x) {ll a; is >> a; x = a; return is; }
inline std::istream& operator>>(std::istream& is, atcoder::modint1000000007& x) {ll a; is >> a; x = a; return is; }
inline std::ostream& operator<<(std::ostream& os, const atcoder::modint& x) { os << x.val(); return os; }
inline std::ostream& operator<<(std::ostream& os, const atcoder::modint998244353& x) { os << x.val(); return os; }
inline std::ostream& operator<<(std::ostream& os, const atcoder::modint1000000007& x) { os << x.val(); return os; }
using modint998244353 = atcoder::modint998244353;
using modint1000000007 = atcoder::modint1000000007;
using modint = atcoder::modint;
/**
 * @brief modint.hpp
 * @docs docs/math/modint.md
 */
#line 3 "/home/seekworser/.cpp_lib/competitive_library/competitive/std/io.hpp"
// 演算子オーバーロード(プロトタイプ宣言)
template <class T, class U> inline istream& operator>>(istream& is, pair<T, U>& p);
template <class T> inline istream& operator>>(istream& is, vector<T>& v);
template <class T, class U> inline ostream& operator<<(ostream& os, const pair<T, U>& p);
template <class T> inline ostream& operator<<(ostream& os, const vector<T>& v);
template <typename T, typename S> ostream &operator<<(ostream &os, const map<T, S> &mp);
template <typename T> ostream &operator<<(ostream &os, const set<T> &st);
template <typename T> ostream &operator<<(ostream &os, const multiset<T> &st);
template <typename T> ostream &operator<<(ostream &os, queue<T> q);
template <typename T> ostream &operator<<(ostream &os, deque<T> q);
template <typename T> ostream &operator<<(ostream &os, stack<T> st);
template <class T, class Container, class Compare> ostream &operator<<(ostream &os, priority_queue<T, Container, Compare> pq);

// 演算子オーバーロード
template <class T, class U> inline istream& operator>>(istream& is, pair<T, U>& p) { is >> p.first >> p.second; return is; }
template <class T> inline istream& operator>>(istream& is, vector<T>& v) { repe(x, v) is >> x; return is; }
template <class T, class U> inline ostream& operator<<(ostream& os, const pair<T, U>& p) { os << p.first << " " << p.second; return os; }
template <class T> inline ostream& operator<<(ostream& os, const vector<T>& v) { rep(i, sz(v)) { os << v.at(i); if (i != sz(v) - 1) os << " "; } return os; }
template <typename T, typename S> ostream &operator<<(ostream &os, const map<T, S> &mp) { for (auto &[key, val] : mp) { os << key << ":" << val << " "; } return os; }
template <typename T> ostream &operator<<(ostream &os, const set<T> &st) { auto itr = st.begin(); for (int i = 0; i < (int)st.size(); i++) { os << *itr << (i + 1 != (int)st.size() ? " " : ""); itr++; } return os; }
template <typename T> ostream &operator<<(ostream &os, const multiset<T> &st) { auto itr = st.begin(); for (int i = 0; i < (int)st.size(); i++) { os << *itr << (i + 1 != (int)st.size() ? " " : ""); itr++; } return os; }
template <typename T> ostream &operator<<(ostream &os, queue<T> q) { while (q.size()) { os << q.front() << " "; q.pop(); } return os; }
template <typename T> ostream &operator<<(ostream &os, deque<T> q) { while (q.size()) { os << q.front() << " "; q.pop_front(); } return os; }
template <typename T> ostream &operator<<(ostream &os, stack<T> st) { while (st.size()) { os << st.top() << " "; st.pop(); } return os; }
template <class T, class Container, class Compare> ostream &operator<<(ostream &os, priority_queue<T, Container, Compare> pq) { while (pq.size()) { os << pq.top() << " "; pq.pop(); } return os; }
template <class T> inline vector<T>& operator--(vector<T>& v) { repe(x, v) --x; return v; }
template <class T> inline vector<T>& operator++(vector<T>& v) { repe(x, v) ++x; return v; }

template <typename T> void print_sep_end(string sep, string end, const T& val) { (void)sep; cout << val << end; };
template <typename T1, typename... T2> void print_sep_end(string sep, string end, const T1 &val, const T2 &...remain) {
    cout << val << sep;
    print_sep_end(sep, end, remain...);
};
template <typename... T> void print(const T&...args) {print_sep_end(" ", "\n", args...);};
#define debug(...) debug_func(0, #__VA_ARGS__, __VA_ARGS__) // debug print
#ifdef LOCAL_TEST
template <typename T>
void debug_func(int i, T name) { (void)i; (void)name; cerr << endl; }
template <typename T1, typename T2, typename... T3> void debug_func(int i, const T1 &name, const T2 &a, const T3 &...b) {
    for ( ; name[i] != ',' && name[i] != '\0'; i++ ) cerr << name[i];
    cerr << ":" << a << " ";
    debug_func(i + 1, name, b...);
}
#endif
#ifndef LOCAL_TEST
template <typename... T>
void debug_func(const T &...) {}
#endif
/**
 * @brief io.hpp
 * @docs docs/std/io.md
 */
#line 6 "answer.cpp"

int main() {
    using mint = modint998244353;
    ll h,w,k;
    cin >> h >> w >> k;
    Combination c(1000001, MODINT998244353);
    mint ans = 0;
    vl div = divisor(k);
    repe(p1, div) {
        ll p2 = k / p1;
        debug(p1, p2);
        if (p1 > h || p2 > w) continue;
        ans += mint(c(h, p1)) * mint(c(w, p2));
    }
    print(ans);
}
0