結果
問題 | No.1978 Permutation Repetition |
ユーザー | Forested |
提出日時 | 2022-06-10 23:16:58 |
言語 | C++17 (gcc 13.3.0 + boost 1.87.0) |
結果 |
WA
|
実行時間 | - |
コード長 | 10,948 bytes |
コンパイル時間 | 1,637 ms |
コンパイル使用メモリ | 139,948 KB |
最終ジャッジ日時 | 2025-01-29 20:18:12 |
ジャッジサーバーID (参考情報) |
judge3 / judge2 |
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ファイルパターン | 結果 |
---|---|
sample | AC * 2 |
other | AC * 32 WA * 12 |
ソースコード
#ifndef LOCAL#define FAST_IO#endif// ===== template.hpp =====#include <algorithm>#include <array>#include <bitset>#include <cassert>#include <cmath>#include <iomanip>#include <iostream>#include <list>#include <map>#include <numeric>#include <queue>#include <random>#include <set>#include <stack>#include <string>#include <tuple>#include <unordered_map>#include <unordered_set>#include <utility>#include <vector>#define OVERRIDE(a, b, c, d, ...) d#define REP2(i, n) for (i32 i = 0; i < (i32) (n); ++i)#define REP3(i, m, n) for (i32 i = (i32) (m); i < (i32) (n); ++i)#define REP(...) OVERRIDE(__VA_ARGS__, REP3, REP2)(__VA_ARGS__)#define PER(i, n) for (i32 i = (i32) (n) - 1; i >= 0; --i)#define ALL(x) begin(x), end(x)using namespace std;using u32 = unsigned int;using u64 = unsigned long long;using u128 = __uint128_t;using i32 = signed int;using i64 = signed long long;using i128 = __int128_t;using f64 = double;using f80 = long double;template <typename T>using Vec = vector<T>;template <typename T>bool chmin(T &x, const T &y) {if (x > y) {x = y;return true;}return false;}template <typename T>bool chmax(T &x, const T &y) {if (x < y) {x = y;return true;}return false;}istream &operator>>(istream &is, i128 &x) {i64 v;is >> v;x = v;return is;}ostream &operator<<(ostream &os, i128 x) {os << (i64) x;return os;}istream &operator>>(istream &is, u128 &x) {u64 v;is >> v;x = v;return is;}ostream &operator<<(ostream &os, u128 x) {os << (u64) x;return os;}template <typename F, typename Comp = less<>>Vec<i32> sort_index(i32 n, F f, Comp comp = Comp()) {Vec<i32> idx(n);iota(ALL(idx), 0);sort(ALL(idx), [&](i32 i, i32 j) -> bool {return comp(f(i), f(j));});return idx;}[[maybe_unused]] constexpr i32 INF = 1000000100;[[maybe_unused]] constexpr i64 INF64 = 3000000000000000100;#ifdef FAST_IO__attribute__((constructor)) void fast_io() {ios::sync_with_stdio(false);cin.tie(nullptr);cout << fixed << setprecision(10);}#endif// ===== template.hpp =====#ifdef DEBUGF#include "cpl/template/debug.hpp"#else#define DBG(x) (void) 0#endif// ===== mod_int.hpp =====#include <cassert>#include <iostream>#include <type_traits>// ===== utils.hpp =====constexpr bool is_prime(unsigned n) {if (n == 0 || n == 1) {return false;}for (unsigned i = 2; i * i <= n; ++i) {if (n % i == 0) {return false;}}return true;}constexpr unsigned mod_pow(unsigned x, unsigned y, unsigned mod) {unsigned ret = 1, self = x;while (y != 0) {if (y & 1) {ret = static_cast<unsigned>(static_cast<unsigned long long>(ret) * self % mod);}self = static_cast<unsigned>(static_cast<unsigned long long>(self) * self % mod);y /= 2;}return ret;}template <unsigned mod>constexpr unsigned primitive_root() {static_assert(is_prime(mod), "`mod` must be a prime number.");if (mod == 2) {return 1;}unsigned primes[32] = {};int it = 0;{unsigned m = mod - 1;for (unsigned i = 2; i * i <= m; ++i) {if (m % i == 0) {primes[it++] = i;while (m % i == 0) {m /= i;}}}if (m != 1) {primes[it++] = m;}}for (unsigned i = 2; i < mod; ++i) {bool ok = true;for (int j = 0; j < it; ++j) {if (mod_pow(i, (mod - 1) / primes[j], mod) == 1) {ok = false;break;}}if (ok)return i;}return 0;}// y >= 1template <typename T>constexpr T safe_mod(T x, T y) {x %= y;if (x < 0) {x += y;}return x;}// y != 0template <typename T>constexpr T floor_div(T x, T y) {if (y < 0) {x *= -1;y *= -1;}if (x >= 0) {return x / y;} else {return -((-x + y - 1) / y);}}// y != 0template <typename T>constexpr T ceil_div(T x, T y) {if (y < 0) {x *= -1;y *= -1;}if (x >= 0) {return (x + y - 1) / y;} else {return -(-x / y);}}// ===== utils.hpp =====template <unsigned mod>class ModInt {static_assert(mod != 0, "`mod` must not be equal to 0.");static_assert(mod < (1u << 31),"`mod` must be less than (1u << 31) = 2147483648.");unsigned val;public:constexpr ModInt() : val(0) {}template <typename T>constexpr ModInt(T x) : val(static_cast<unsigned>(safe_mod(x, static_cast<T>(mod)))) {}static constexpr ModInt raw(unsigned x) {ModInt<mod> ret;ret.val = x;return ret;}constexpr unsigned get_val() const {return val;}constexpr ModInt operator+() const {return *this;}constexpr ModInt operator-() const {return ModInt<mod>(0u) - *this;}constexpr ModInt &operator+=(const ModInt &rhs) {val += rhs.val;if (val >= mod)val -= mod;return *this;}constexpr ModInt &operator-=(const ModInt &rhs) {if (val < rhs.val)val += mod;val -= rhs.val;return *this;}constexpr ModInt &operator*=(const ModInt &rhs) {val = (unsigned long long)val * rhs.val % mod;return *this;}constexpr ModInt &operator/=(const ModInt &rhs) {val = (unsigned long long)val * rhs.inv().val % mod;return *this;}friend constexpr ModInt operator+(const ModInt &lhs, const ModInt &rhs) {return ModInt<mod>(lhs) += rhs;}friend constexpr ModInt operator-(const ModInt &lhs, const ModInt &rhs) {return ModInt<mod>(lhs) -= rhs;}friend constexpr ModInt operator*(const ModInt &lhs, const ModInt &rhs) {return ModInt<mod>(lhs) *= rhs;}friend constexpr ModInt operator/(const ModInt &lhs, const ModInt &rhs) {return ModInt<mod>(lhs) /= rhs;}constexpr ModInt pow(unsigned long long x) const {ModInt<mod> ret = ModInt<mod>::raw(1);ModInt<mod> self = *this;while (x != 0) {if (x & 1)ret *= self;self *= self;x >>= 1;}return ret;}constexpr ModInt inv() const {static_assert(is_prime(mod), "`mod` must be a prime number.");assert(val != 0);return this->pow(mod - 2);}friend std::istream &operator>>(std::istream &is, ModInt<mod> &x) {is >> x.val;x.val %= mod;return is;}friend std::ostream &operator<<(std::ostream &os, const ModInt<mod> &x) {os << x.val;return os;}friend bool operator==(const ModInt &lhs, const ModInt &rhs) {return lhs.val == rhs.val;}friend bool operator!=(const ModInt &lhs, const ModInt &rhs) {return lhs.val != rhs.val;}};[[maybe_unused]] constexpr unsigned mod998244353 = 998244353;[[maybe_unused]] constexpr unsigned mod1000000007 = 1000000007;// ===== mod_int.hpp =====using Mint = ModInt<mod1000000007>;// ===== factorial_table.hpp =====#include <vector>#include <cassert>template <typename T>class FactorialTable {std::vector<T> fac;std::vector<T> ifac;public:FactorialTable() : fac(1, T(1)), ifac(1, T(1)) {}FactorialTable(int n) : fac(n + 1), ifac(n + 1) {assert(n >= 0);fac[0] = T(1);for (int i = 1; i <= n; ++i) {fac[i] = fac[i - 1] * T(i);}ifac[n] = T(1) / T(fac[n]);for (int i = n; i > 0; --i) {ifac[i - 1] = ifac[i] * T(i);}}void resize(int n) {int old = n_max();if (n <= old) {return;}fac.resize(n + 1);for (int i = old + 1; i <= n; ++i) {fac[i] = fac[i - 1] * T(i);}ifac.resize(n + 1);ifac[n] = T(1) / T(fac[n]);for (int i = n; i > old; --i) {ifac[i - 1] = ifac[i] * T(i);}}inline int n_max() const {return static_cast<int>(fac.size() - 1);}inline T fact(int n) const {assert(n >= 0 && n <= n_max());return fac[n];}inline T inv_fact(int n) const {assert(n >= 0 && n <= n_max());return ifac[n];}inline T choose(int n, int k) const {assert(k <= n_max() && n <= n_max());if (k > n || k < 0) {return T(0);}return fac[n] * ifac[k] * ifac[n - k];}inline T multi_choose(int n, int k) const {assert(n >= 1 && k >= 0 && k + n - 1 <= n_max());return choose(k + n - 1, k);}inline T n_terms_sum_k(int n, int k) const {assert(n >= 0);if (k < 0) {return T(0);}if (n == 0) {return k == 0 ? T(1) : T(0);}return choose(n + k - 1, n - 1);}};// ===== factorial_table.hpp =====int main() {i32 n, m;cin >> n >> m;Vec<i32> a(n);REP(i, n) {cin >> a[i];--a[i];}FactorialTable<Mint> table(n);Vec<i32> cycle_cnt(n + 1, 0);{Vec<bool> checked(n, false);REP(i, n) {if (checked[i]) {continue;}i32 cur = i, cnt = 0;while (!checked[cur]) {checked[cur] = true;++cnt;cur = a[cur];}++cycle_cnt[cnt];}}DBG(cycle_cnt);Vec<Vec<pair<i32, Mint>>> gens(n + 1);REP(i, 1, n + 1) {i32 gc = gcd(i, m);gens[i / gc].emplace_back(gc, Mint(i / gc).pow(gc - 1));}DBG(gens);Mint ans(1);REP(i, 1, n + 1) {Vec<Mint> dp(cycle_cnt[i] + 1);dp[0] = Mint(1);for (auto [cnt, wgt] : gens[i]) {Vec<Mint> ndp(cycle_cnt[i] + 1);REP(j, cycle_cnt[i] + 1) {for (i32 k = 0; j + k * cnt <= cycle_cnt[i]; ++k) {ndp[j + k * cnt] += dp[j] * table.choose(cycle_cnt[i] - j, k * cnt) * table.fact(k * cnt) * table.inv_fact(cnt).pow(k) * table.inv_fact(k) * wgt.pow(k);}}/*REP(j, cycle_cnt[i] - cnt + 1) {dp[j + cnt] += dp[j] * wgt * table.inv_fact(cnt);}*/dp = ndp;DBG(dp);}DBG(dp);ans *= dp[cycle_cnt[i]];//ans *= dp[cycle_cnt[i]] * table.fact(cycle_cnt[i]);}cout << ans << '\n';}