結果

問題 No.377 背景パターン
ユーザー cureskolcureskol
提出日時 2024-09-15 19:35:12
言語 C++23
(gcc 12.3.0 + boost 1.83.0)
結果
AC  
実行時間 589 ms / 5,000 ms
コード長 9,984 bytes
コンパイル時間 3,697 ms
コンパイル使用メモリ 268,196 KB
実行使用メモリ 5,376 KB
最終ジャッジ日時 2024-09-15 19:35:18
合計ジャッジ時間 5,709 ms
ジャッジサーバーID
（参考情報） 		judge4 / judge6
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 2 ms
5,248 KB
testcase_01 AC 2 ms
5,376 KB
testcase_02 AC 2 ms
5,376 KB
testcase_03 AC 2 ms
5,376 KB
testcase_04 AC 2 ms
5,376 KB
testcase_05 AC 2 ms
5,376 KB
testcase_06 AC 2 ms
5,376 KB
testcase_07 AC 2 ms
5,376 KB
testcase_08 AC 2 ms
5,376 KB
testcase_09 AC 3 ms
5,376 KB
testcase_10 AC 2 ms
5,376 KB
testcase_11 AC 2 ms
5,376 KB
testcase_12 AC 2 ms
5,376 KB
testcase_13 AC 5 ms
5,376 KB
testcase_14 AC 5 ms
5,376 KB
testcase_15 AC 2 ms
5,376 KB
testcase_16 AC 589 ms
5,376 KB
testcase_17 AC 572 ms
5,376 KB
testcase_18 AC 2 ms
5,376 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 # 

#pragma region template
#ifdef USE_PRECOMPILE
#include "pch.h"
#else
#pragma GCC optimize("Ofast")
#include <bits/stdc++.h>
using namespace std;

using ll = long long;
using ld = long double;
using vi = std::vector<int>;
using vll = std::vector<ll>;
template <typename T> using PA = std::pair<T, T>;
using pi = PA<int>;
using pll = PA<ll>;

#define overload2(a, b, c, ...) c
#define overload3(a, b, c, d, ...) d
#define overload4(a, b, c, d, e, ...) e
#define overload5(a, b, c, d, e, f, ...) f

#define TYPE1(T) template <typename T>
#define TYPE2(T, U) template <typename T, typename U>
#define TYPE(...) overload2(__VA_ARGS__, TYPE2, TYPE1)(__VA_ARGS__)
#define TYPES1(T) template <typename... T>
#define TYPES2(H, T) template <typename H, typename... T>
#define TYPES(...) overload2(__VA_ARGS__, TYPES2, TYPES1)(__VA_ARGS__)

#define REP4(i, s, n, d) for (int i = (s); i < (n); i += (d))
#define REP3(i, s, n) REP4(i, s, n, 1)
#define REP2(i, n) REP3(i, 0, n)
#define REP1(n) REP2(tomato, n)
#define REP(...) overload4(__VA_ARGS__, REP4, REP3, REP2, REP1)(__VA_ARGS__)

#define RREP4(i, n, s, d) for (int i = (n) - 1; i >= (s); i -= (d))
#define RREP3(i, n, s) RREP4(i, n, s, 1)
#define RREP2(i, n) RREP3(i, n, 0)
#define RREP1(n) RREP2(tomato, n)
#define RREP(...)                                                              \
    overload4(__VA_ARGS__, RREP4, RREP3, RREP2, RREP1)(__VA_ARGS__)

#define FOR4(a, b, c, d, v) for (auto [a, b, c, d] : v)
#define FOR3(a, b, c, v) for (auto [a, b, c] : v)
#define FOR2(a, b, v) for (auto [a, b] : v)
#define FOR1(a, v) for (auto a : v)
#define FOR(...) overload5(__VA_ARGS__, FOR4, FOR3, FOR2, FOR1)(__VA_ARGS__)

#define AFOR4(a, b, c, d, v) for (auto &[a, b, c, d] : v)
#define AFOR3(a, b, c, v) for (auto &[a, b, c] : v)
#define AFOR2(a, b, v) for (auto &[a, b] : v)
#define AFOR1(a, v) for (auto &a : v)
#define AFOR(...)                                                              \
    overload5(__VA_ARGS__, AFOR4, AFOR3, AFOR2, AFOR1)(__VA_ARGS__)

#define CFOR4(a, b, c, d, v) for (const auto &[a, b, c, d] : v)
#define CFOR3(a, b, c, v) for (const auto &[a, b, c] : v)
#define CFOR2(a, b, v) for (const auto &[a, b] : v)
#define CFOR1(a, v) for (const auto &a : v)
#define CFOR(...)                                                              \
    overload5(__VA_ARGS__, CFOR4, CFOR3, CFOR2, CFOR1)(__VA_ARGS__)

#define RFOR4(a, b, c, d, v) for (auto [a, b, c, d] : v | std::views::reverse)
#define RFOR3(a, b, c, v) for (auto [a, b, c] : v | std::views::reverse)
#define RFOR2(a, b, v) for (auto [a, b] : v | std::views::reverse)
#define RFOR1(a, v) for (auto a : v | std::views::reverse)
#define RFOR(...)                                                              \
    overload5(__VA_ARGS__, RFOR4, RFOR3, RFOR2, RFOR1)(__VA_ARGS__)

#define RAFOR4(a, b, c, d, v) for (auto &[a, b, c, d] : v | std::views::reverse)
#define RAFOR3(a, b, c, v) for (auto &[a, b, c] : v | std::views::reverse)
#define RAFOR2(a, b, v) for (auto &[a, b] : v | std::views::reverse)
#define RAFOR1(a, v) for (auto &a : v | std::views::reverse)
#define RAFOR(...)                                                             \
    overload5(__VA_ARGS__, RAFOR4, RAFOR3, RAFOR2, RAFOR1)(__VA_ARGS__)

#define RCFOR4(a, b, c, d, v)                                                  \
    for (const auto &[a, b, c, d] : v | std::views::reverse)
#define RCFOR3(a, b, c, v) for (const auto &[a, b, c] : v | std::views::reverse)
#define RCFOR2(a, b, v) for (const auto &[a, b] : v | std::views::reverse)
#define RCFOR1(a, v) for (const auto &a : v | std::views::reverse)
#define RCFOR(...)                                                             \
    overload5(__VA_ARGS__, RCFOR4, RCFOR3, RCFOR2, RCFOR1)(__VA_ARGS__)

#define ALL(v) v.begin(), v.end()
#define RALL(v) v.rbegin(), v.rend()
#define SORT(v) std::ranges::sort(v)
#define RSORT(v) sort(RALL(v))
#define REVERSE(v) std::ranges::reverse(v)
#define UNIQUE(v) SORT(v), v.erase(unique(ALL(v)), v.end())
#define SZ(v) int(v.size())
#define MAX(v) std::ranges::max(v)
#define MIN(v) std::ranges::min(v)
template <typename T>
std::conditional_t<std::is_same_v<T, int>, ll, T> SUM(const std::vector<T> &v) {
    return std::accumulate(
        ALL(v), std::conditional_t<std::is_same_v<T, int>, ll, T>(0));
}

TYPES(T) void input(T &...a) { (std::cin >> ... >> a); }
#define DECLARE(T, ...)                                                        \
    T __VA_ARGS__;                                                             \
    input(__VA_ARGS__);
#define INT(...) DECLARE(int, __VA_ARGS__)
#define STR(...) DECLARE(std::string, __VA_ARGS__)
#define LL(...) DECLARE(long long, __VA_ARGS__)
#define CHR(...) DECLARE(char, __VA_ARGS__)
#define DBL(...) DECLARE(double, __VA_ARGS__)
#define VI(n, v)                                                               \
    vi v(n);                                                                   \
    std::cin >> v;
#define VLL(n, v)                                                              \
    vll v(n);                                                                  \
    std::cin >> v;
#define VS(n, s)                                                               \
    std::vector<std::string> s(n);                                             \
    std::cin >> s;

TYPE(T, S) std::istream &operator>>(std::istream &is, std::pair<T, S> &p) {
    is >> p.first >> p.second;
    return is;
}
TYPE(T, S)
std::ostream &operator<<(std::ostream &os, const std::pair<T, S> &p) {
    os << p.first << " " << p.second;
    return os;
}
TYPE(T) istream &operator>>(std::istream &is, std::vector<T> &v) {
    for (auto &a : v)
        std::cin >> a;
    return is;
}
TYPE(T) std::ostream &operator<<(std::ostream &os, const std::vector<T> &v) {
    if (&os == &std::cerr)
        os << "[";
    REP (i, v.size()) {
        os << v[i];
        if (i + 1 < v.size())
            os << (&os == &std::cerr ? "," : " ");
    }
    if (&os == &std::cerr)
        os << "]";
    return os;
}

#ifdef __DEBUG
#include <debug>
#else
#define debug(...) void(0)
#endif

void print() { cout << '\n'; }
TYPES(T, Ts) void print(const T &a, const Ts &...b) {
    std::cout << a;
    (std::cout << ... << (std::cout << ' ', b));
    std::cout << '\n';
}

TYPE(T) using pq = std::priority_queue<T>;
TYPE(T) using pqg = std::priority_queue<T, std::vector<T>, std::greater<T>>;
TYPE(T) T pick(std::queue<T> &que) {
    assert(que.size());
    T a = que.front();
    que.pop();
    return a;
}
TYPE(T) T pick(pq<T> &que) {
    assert(que.size());
    T a = que.top();
    que.pop();
    return a;
}
TYPE(T) T pick(pqg<T> &que) {
    assert(que.size());
    T a = que.top();
    que.pop();
    return a;
}
TYPE(T) T pick(std::stack<T> &sta) {
    assert(sta.size());
    T a = sta.top();
    sta.pop();
    return a;
}
TYPE(T) void clear(T &v) { v = decltype(v)(); }

std::string YES(bool f = true) { return (f ? "YES" : "NO"); }
std::string Yes(bool f = true) { return (f ? "Yes" : "No"); }
std::string yes(bool f = true) { return (f ? "yes" : "no"); }

constexpr int INF = 1e9 + 7;
constexpr ll LINF = ll(1e18) + 7;
constexpr ld EPS = 1e-10;

vi iota(int n) {
    vi a(n);
    std::iota(ALL(a), 0);
    return a;
}
TYPE(T) void add(std::vector<T> &v, T a = 1) {
    AFOR (p, v)
        p += a;
}
TYPE(T) T rev(T a) {
    REVERSE(a);
    return a;
}
TYPE(T) void fin(T a) {
    std::cout << a << '\n';
    exit(0);
}
TYPE(T) bool chmax(T &a, T b) { return (a < b && (a = b, true)); }
TYPE(T) bool chmin(T &a, T b) { return (a > b && (a = b, true)); }
TYPES(T, Ns) auto make_vector(T x, int n, Ns... ns) {
    if constexpr (sizeof...(ns) == 0)
        return std::vector<T>(n, x);
    else
        return std::vector(n, make_vector<T>(x, ns...));
}
bool in(const ll S, const int a) { return (S >> a) & 1; }
int digit(char c) { return (c >= '0' and c <= '9' ? c - '0' : -1); }

void signal_hander(int signal) { std::exit(EXIT_FAILURE); }
#endif
#pragma endregion template

#include <atcoder/modint>
using namespace atcoder;
using mint = modint1000000007;
namespace atcoder {
ostream &operator<<(ostream &os, mint a) {
    os << a.val();
    return os;
}
istream &operator>>(istream &is, mint &a) {
    long long b;
    is >> b;
    a = b;
    return is;
}
} // namespace atcoder

struct D {
    int n;

    int pow(int n, int k) {
        int res = 1;
        while (k--)
            res *= n;
        return res;
    }

  public:
    std::vector<std::pair<int, int>> prime_factor;
    std::vector<int> divisors;

    D(int n) : n(n) {
        int N = n;
        for (int i = 2; i * i <= N; i++) {
            if (N % i)
                continue;
            prime_factor.emplace_back(i, 0);
            while (N % i == 0) {
                prime_factor.back().second++;
                N /= i;
            }
        }
        if (N > 1)
            prime_factor.emplace_back(N, 1);
        debug(prime_factor);

        int prod = 1;
        for (const auto &[p, e] : prime_factor)
            prod *= e + 1;

        for (int S : std::views::iota(0, prod)) {
            int x = 1;
            for (const auto &[p, e] : prime_factor) {
                x *= pow(p, S % (e + 1));
                S /= e + 1;
            }
            divisors.push_back(x);
        }

        debug(divisors);
    }

    int phi(int d) {
        int res = d;
        for (const auto &[p, _] : prime_factor)
            if (d % p == 0)
                (res /= p) *= p - 1;
        return res;
    }
};

int main() {
    std::ios::sync_with_stdio(false);
    std::cin.tie(nullptr);
    std::signal(SIGABRT, signal_hander);

    INT(h, w, k);

    D H(h), W(w), HW(std::gcd(h, w));

    mint ans = 0;
    for (int x : H.divisors) {
        for (int y : W.divisors) {
            ans +=
                mint::raw(k).pow(h * ll(w) / std::lcm<ll, ll>(h / x, w / y)) *
                H.phi(h / x) * W.phi(w / y);
        }
    }

    std::cout << ans / (h * mint(w)) << '\n';
}
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