結果

問題 No.2527 H and W
ユーザー pmankiraipmankirai
提出日時 2023-11-03 22:47:52
言語 C++17
(gcc 12.3.0 + boost 1.83.0)
結果
AC  
実行時間 28 ms / 2,000 ms
コード長 9,662 bytes
コンパイル時間 2,125 ms
コンパイル使用メモリ 206,472 KB
実行使用メモリ 11,104 KB
最終ジャッジ日時 2024-09-25 21:11:34
合計ジャッジ時間 3,547 ms
ジャッジサーバーID
（参考情報） 		judge3 / judge4
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 1 ms
5,248 KB
testcase_01 AC 2 ms
5,376 KB
testcase_02 AC 24 ms
11,008 KB
testcase_03 AC 2 ms
5,376 KB
testcase_04 AC 25 ms
11,008 KB
testcase_05 AC 24 ms
10,880 KB
testcase_06 AC 26 ms
11,008 KB
testcase_07 AC 2 ms
5,376 KB
testcase_08 AC 26 ms
11,008 KB
testcase_09 AC 14 ms
11,008 KB
testcase_10 AC 13 ms
10,864 KB
testcase_11 AC 23 ms
10,988 KB
testcase_12 AC 23 ms
11,008 KB
testcase_13 AC 25 ms
11,004 KB
testcase_14 AC 25 ms
11,008 KB
testcase_15 AC 25 ms
11,008 KB
testcase_16 AC 28 ms
11,060 KB
testcase_17 AC 25 ms
11,052 KB
testcase_18 AC 24 ms
10,952 KB
testcase_19 AC 16 ms
7,936 KB
testcase_20 AC 16 ms
8,664 KB
testcase_21 AC 24 ms
11,076 KB
testcase_22 AC 24 ms
11,008 KB
testcase_23 AC 23 ms
11,104 KB
testcase_24 AC 16 ms
8,192 KB
testcase_25 AC 13 ms
9,824 KB
権限があれば一括ダウンロードができます

ソースコード

diff # 

#include <bits/stdc++.h>
using namespace std;
#define rep(i, n) for (int i = 0; i < (n); i++)
#define rep1(i, n) for (int i = 1; i <= (n); i++)
#define rrep(i, n) for (int i = n - 1; i >= 0; i--)
#define rrep1(i, n) for (int i = n; i >= 1; i--)
#define all(x) x.begin(), x.end()
#define rall(x) x.rbegin(), x.rend()
#define eb emplace_back
#define fi first
#define se second
#define sz(x) (int)(x).size()
template <class T> using V = vector<T>;
template <class T> using VV = V<V<T>>;
typedef long long int ll;

void speedUpIO() {
    cin.tie(nullptr);
    ios::sync_with_stdio(false);
}

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;
}

#ifndef ATCODER_MODINT_HPP
#define ATCODER_MODINT_HPP 1

#include <atcoder/internal_math>
#include <atcoder/internal_type_traits>
#include <cassert>
#include <numeric>
#include <type_traits>

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

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());
    }
    static_modint(bool 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());
    }
    dynamic_modint(bool 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

#endif  // ATCODER_MODINT_HPP

/*--------------------------------------------------*/
typedef pair<int, int> P;
typedef atcoder::modint998244353 mint;

const int INF = 1e9;
const ll LINF = 1e18;
const int MX = 100010;

// combination mod prime
struct combination {
    V<mint> fact, ifact;
    combination(int n) : fact(n + 1), ifact(n + 1) {
        fact[0] = 1;
        for (int i = 1; i <= n; ++i) fact[i] = fact[i - 1] * i;
        ifact[n] = fact[n].inv();
        for (int i = n; i >= 1; --i) ifact[i - 1] = ifact[i] * i;
    }
    mint nCk(int n, int k) {
        if (k < 0 || k > n) return 0;
        return fact[n] * ifact[k] * ifact[n - k];
    }
};

void solve() {
    ll H, W, K;
    cin >> H >> W >> K;
    K = H * W - K;
    mint ans = 0;
    combination cmb(max(H, W));
    if (K == H * W) {
        rep(w, W + 1) ans += cmb.nCk(W, w);
        rep(h, H + 1) ans += cmb.nCk(H, h);
        ans -= 1;
        cout << ans.val() << endl;
        return;
    }
    rep(h, H) {
        if ((K - W * h) % (H - h) != 0) continue;
        ll w = (K - W * h) / (H - h);
        if (!(0 <= w && w <= W)) continue;
        ans += cmb.nCk(H, h) * cmb.nCk(W, w);
    }
    cout << ans.val() << endl;
}

int main() {
    speedUpIO();
    int t = 1;
    // cin >> t;
    while (t--) {
        solve();
        // cout << solve() << "\n";
        // cout << (solve() ? "YES" : "NO") << "\n";
        // cout << fixed << setprecision(15) << solve() << "\n";
    }
    return 0;
}
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