結果
問題 | No.1978 Permutation Repetition |
ユーザー | haruki_K |
提出日時 | 2022-06-10 23:11:52 |
言語 | C++17 (gcc 13.3.0 + boost 1.87.0) |
結果 |
AC
|
実行時間 | 4 ms / 2,000 ms |
コード長 | 11,027 bytes |
コンパイル時間 | 2,514 ms |
コンパイル使用メモリ | 219,424 KB |
最終ジャッジ日時 | 2025-01-29 20:16:38 |
ジャッジサーバーID (参考情報) |
judge4 / judge3 |
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ファイルパターン | 結果 |
---|---|
sample | AC * 2 |
other | AC * 44 |
ソースコード
// >>> TEMPLATES#include <bits/stdc++.h>using namespace std;using ll = long long;using ld = long double;using i32 = int32_t;using i64 = int64_t;using u32 = uint32_t;using u64 = uint64_t;#define int ll#define rep(i, n) for (int i = 0; i < (int)(n); i++)#define rep1(i, n) for (int i = 1; i <= (int)(n); i++)#define repR(i, n) for (int i = (int)(n)-1; i >= 0; i--)#define rep1R(i, n) for (int i = (int)(n); i >= 1; i--)#define loop(i, a, B) for (int i = a; i B; i++)#define loopR(i, a, B) for (int i = a; i B; i--)#define all(x) begin(x), end(x)#define allR(x) rbegin(x), rend(x)#define pb push_back#define eb emplace_back#define fst first#define snd secondtemplate <class Int> auto constexpr inf_ = numeric_limits<Int>::max()/2-1;auto constexpr INF32 = inf_<int32_t>;auto constexpr INF64 = inf_<int64_t>;auto constexpr INF = inf_<int>;#ifdef LOCAL#include "debug.hpp"#define oj_local(x, y) (y)#else#define dump(...) (void)(0)#define say(x) (void)(0)#define debug if (0)#define oj_local(x, y) (x)#endiftemplate <class T, class Comp> struct pque : priority_queue<T, vector<T>, Comp> { vector<T> &data() { return this->c; } void clear() { this->c.clear(); } };template <class T> using pque_max = pque<T, less<T>>;template <class T> using pque_min = pque<T, greater<T>>;template <class T, class = typename T::iterator, enable_if_t<!is_same<T, string>::value, int> = 0>ostream& operator<<(ostream& os, T const& a) { bool f = true; for (auto const& x : a) os << (f ? "" : " ") << x, f = false; return os; }template <class T, size_t N, enable_if_t<!is_same<T, char>::value, int> = 0>ostream& operator<<(ostream& os, const T (&a)[N]) { bool f = true; for (auto const& x : a) os << (f ? "" : " ") << x, f = false; return os; }template <class T, class = decltype(begin(declval<T&>())), class = typename enable_if<!is_same<T, string>::value>::type>istream& operator>>(istream& is, T &a) { for (auto& x : a) is >> x; return is; }template <class T, class S> ostream& operator<<(ostream& os, pair<T, S> const& p) { return os << p.first << " " << p.second; }template <class T, class S> istream& operator>>(istream& is, pair<T, S>& p) { return is >> p.first >> p.second; }struct IOSetup { IOSetup() { cin.tie(nullptr); ios::sync_with_stdio(false); cout << fixed << setprecision(15); } } iosetup;template <class F> struct FixPoint : private F {constexpr FixPoint(F&& f) : F(forward<F>(f)) {}template <class... T> constexpr auto operator()(T&&... x) const { return F::operator()(*this, forward<T>(x)...); }};struct MakeFixPoint { template <class F> constexpr auto operator|(F&& f) const { return FixPoint<F>(forward<F>(f)); } };#define MFP MakeFixPoint()|#define def(name, ...) auto name = MFP [&](auto &&name, __VA_ARGS__)template <class T, size_t d> struct vec_impl {using type = vector<typename vec_impl<T, d-1>::type>;template <class... U> static type make_v(size_t n, U&&... x) { return type(n, vec_impl<T, d-1>::make_v(forward<U>(x)...)); }};template <class T> struct vec_impl<T, 0> { using type = T; static type make_v(T const& x = {}) { return x; } };template <class T, size_t d = 1> using vec = typename vec_impl<T, d>::type;template <class T, size_t d = 1, class... Args> auto make_v(Args&&... args) { return vec_impl<T, d>::make_v(forward<Args>(args)...); }template <class T> void quit(T const& x) { cout << x << endl; exit(0); }template <class T, class U> constexpr bool chmin(T& x, U const& y) { if (x > (T)y) { x = (T)y; return true; } return false; }template <class T, class U> constexpr bool chmax(T& x, U const& y) { if (x < (T)y) { x = (T)y; return true; } return false; }template <class It> constexpr auto sumof(It b, It e) { return accumulate(b, e, typename iterator_traits<It>::value_type{}); }template <class T> int sz(T const& x) { return x.size(); }template <class C, class T> int lbd(C const& v, T const& x) { return lower_bound(begin(v), end(v), x)-begin(v); }template <class C, class T> int ubd(C const& v, T const& x) { return upper_bound(begin(v), end(v), x)-begin(v); }constexpr ll mod(ll x, ll m) { assert(m > 0); return (x %= m) < 0 ? x+m : x; }constexpr ll div_floor(ll x, ll y) { assert(y != 0); return x/y - ((x^y) < 0 and x%y); }constexpr ll div_ceil(ll x, ll y) { assert(y != 0); return x/y + ((x^y) > 0 and x%y); }constexpr int dx[] = { 1, 0, -1, 0, 1, -1, -1, 1 };constexpr int dy[] = { 0, 1, 0, -1, 1, 1, -1, -1 };constexpr int popcnt(ll x) { return __builtin_popcountll(x); }mt19937_64 seed_{random_device{}()};template <class Int> Int rand(Int a, Int b) { return uniform_int_distribution<Int>(a, b)(seed_); }i64 irand(i64 a, i64 b) { return rand<i64>(a, b); } // [a, b]u64 urand(u64 a, u64 b) { return rand<u64>(a, b); } //template <class It> void shuffle(It l, It r) { shuffle(l, r, seed_); }template <class V> V &operator--(V &v) { for (auto &x : v) --x; return v; }template <class V> V &operator++(V &v) { for (auto &x : v) ++x; return v; }bool next_product(vector<int> &v, int m) {repR (i, v.size()) if (++v[i] < m) return true; else v[i] = 0;return false;}bool next_product(vector<int> &v, vector<int> const& s) {repR (i, v.size()) if (++v[i] < s[i]) return true; else v[i] = 0;return false;}template <class vec> int sort_unique(vec &v) {sort(begin(v), end(v));v.erase(unique(begin(v), end(v)), end(v));return v.size();}template <class It> auto prefix_sum(It l, It r) {vector<typename It::value_type> s = { 0 };while (l != r) s.emplace_back(s.back() + *l++);return s;}template <class It> auto suffix_sum(It l, It r) {vector<typename It::value_type> s = { 0 };while (l != r) s.emplace_back(*--r + s.back());reverse(s.begin(), s.end());return s;}template <class T> T pop(vector<T> &a) { auto x = a.back(); a.pop_back(); return x; }template <class T, class V, class C> T pop(priority_queue<T, V, C> &a) { auto x = a.top(); a.pop(); return x; }template <class T> T pop(queue<T> &a) { auto x = a.front(); a.pop(); return x; }template <class T> T pop_front(deque<T> &a) { auto x = a.front(); a.pop_front(); return x; }template <class T> T pop_back(deque<T> &a) { auto x = a.back(); a.pop_back(); return x; }template <class T> T pop_front(set<T> &a) { auto x = *a.begin(); a.erase(a.begin()); return x; }template <class T> T pop_back(set<T> &a) { auto it = prev(a.end()); auto x = *it; a.erase(it); return x; }template <class T> T pop_front(multiset<T> &a) { auto it = a.begin(); auto x = *it; a.erase(it); return x; }template <class T> T pop_back(multiset<T> &a) { auto it = prev(a.end()); auto x = *it; a.erase(it); return x; }// <<<// >>> modinttemplate <uint32_t md>class modint {static_assert(md < (1u<<31), "");using M = modint;using i64 = int64_t;uint32_t x;public:static constexpr uint32_t mod = md;constexpr modint(i64 x = 0) : x((x%=md) < 0 ? x+md : x) { }constexpr i64 val() const { return x; }constexpr explicit operator i64() const { return x; }constexpr bool operator==(M r) const { return x == r.x; }constexpr bool operator!=(M r) const { return x != r.x; }constexpr M operator+() const { return *this; }constexpr M operator-() const { return M()-*this; }constexpr M& operator+=(M r) { x += r.x; x = (x < md ? x : x-md); return *this; }constexpr M& operator-=(M r) { x += md-r.x; x = (x < md ? x : x-md); return *this; }constexpr M& operator*=(M r) { x = (uint64_t(x)*r.x)%md; return *this; }constexpr M& operator/=(M r) { return *this *= r.inv(); }constexpr M operator+(M r) const { return M(*this) += r; }constexpr M operator-(M r) const { return M(*this) -= r; }constexpr M operator*(M r) const { return M(*this) *= r; }constexpr M operator/(M r) const { return M(*this) /= r; }friend constexpr M operator+(i64 x, M y) { return M(x)+y; }friend constexpr M operator-(i64 x, M y) { return M(x)-y; }friend constexpr M operator*(i64 x, M y) { return M(x)*y; }friend constexpr M operator/(i64 x, M y) { return M(x)/y; }constexpr M inv() const { assert(x > 0); return pow(md-2); }constexpr M pow(i64 n) const {assert(not (x == 0 and n == 0));if (n < 0) return inv().pow(-n);M v = *this, r = 1;for (; n > 0; n >>= 1, v *= v) if (n&1) r *= v;return r;}#ifdef LOCALfriend string to_s(M r) { return to_s(r.val(), mod); }#endiffriend ostream& operator<<(ostream& os, M r) { return os << r.val(); }friend istream& operator>>(istream& is, M &r) { i64 x; is >> x; r = x; return is; }};// <<<//constexpr int64_t MOD = 998244353;constexpr int64_t MOD = 1e9+7;using mint = modint<MOD>;mint sign(int n) { return n & 1 ? -1 : +1; }// >>> mod tabletemplate <class mint> struct ModTable {vector<mint> fact, finv;void calc(int n) {int old = fact.size();if (n < old) return;n += 1000;fact.resize(n+1);finv.resize(n+1);if (old == 0) {fact[0] = fact[1] = finv[0] = finv[1] = 1;old = 2;}for (auto i = old; i <= n; i++) fact[i] = fact[i-1] * i;finv[n] = mint(1) / fact[n];for (auto i = n-1; i >= old; i--) finv[i] = finv[i+1] * (i+1);}};ModTable<mint> mod_tab;mint fact(int n) {assert(0 <= n);return mod_tab.calc(n), mod_tab.fact[n];}mint finv(int n) {assert(0 <= n);return mod_tab.calc(n), mod_tab.finv[n];}mint comb(int n, int k) {if (n < 0 || k < 0 || n < k) return 0;mod_tab.calc(n);return mod_tab.fact[n] * mod_tab.finv[k] * mod_tab.finv[n-k];}mint perm(int n, int k) {assert(k >= 0); assert(n >= k);mod_tab.calc(n);return mod_tab.fact[n] * mod_tab.finv[n-k];}// <<<// >>> cycle decompositionvector<vector<int>> cycles(vector<int> const& p) {const int n = p.size();rep (i, n) assert(0 <= p[i]), assert(p[i] < n);vector<bool> used(n);vector<vector<int>> ret;rep (i, n) if (not used[i]) {vector<int> cyc;int x = i;do {cyc.eb(x);used[x] = true;x = p[x];} while (x != i);ret.eb(cyc);}return ret;}// <<<int32_t main() {int n, m; cin >> n >> m;vector<int> a(n); cin >> a; --a;map<int, int> cnt;for (auto const& c : cycles(a)) {cnt[c.size()]++;}mint ans = 1;for (auto [len, num] : cnt) {vector<pair<int, mint>> trans;rep1 (k, num) if (gcd(len*k, m) == k) {trans.eb(k, mint(len).pow(k-1) * fact(k-1));}vector<mint> dp(num+1);dp[0] = 1;rep (j, num) {for (auto [k, val] : trans) {if (j+k <= num) {dp[j+k] += dp[j] * comb(num-j-1, k-1) * val;} else {break;}}}dump(len, num, dp[num], trans);ans *= dp[num];}cout << ans << '\n';}