#include using namespace std; #define rep(i, n) for (int i = 0; i < n; i++) #define rep2(i, x, n) for (int i = x; i <= n; i++) #define rep3(i, x, n) for (int i = x; i >= n; i--) #define each(e, v) for (auto &e : v) #define pb push_back #define eb emplace_back #define all(x) x.begin(), x.end() #define rall(x) x.rbegin(), x.rend() #define sz(x) (int)x.size() using ll = long long; using pii = pair; using pil = pair; using pli = pair; using pll = pair; template bool chmax(T &x, const T &y) { return (x < y) ? (x = y, true) : false; } template bool chmin(T &x, const T &y) { return (x > y) ? (x = y, true) : false; } template int flg(T x, int i) { return (x >> i) & 1; } template void print(const vector &v, T x = 0) { int n = v.size(); for (int i = 0; i < n; i++) cout << v[i] + x << (i == n - 1 ? '\n' : ' '); if (v.empty()) cout << '\n'; } template void printn(const vector &v, T x = 0) { int n = v.size(); for (int i = 0; i < n; i++) cout << v[i] + x << '\n'; } template int lb(const vector &v, T x) { return lower_bound(begin(v), end(v), x) - begin(v); } template int ub(const vector &v, T x) { return upper_bound(begin(v), end(v), x) - begin(v); } template void rearrange(vector &v) { sort(begin(v), end(v)); v.erase(unique(begin(v), end(v)), end(v)); } template vector id_sort(const vector &v, bool greater = false) { int n = v.size(); vector ret(n); iota(begin(ret), end(ret), 0); sort(begin(ret), end(ret), [&](int i, int j) { return greater ? v[i] > v[j] : v[i] < v[j]; }); return ret; } template pair operator+(const pair &p, const pair &q) { return make_pair(p.first + q.first, p.second + q.second); } template pair operator-(const pair &p, const pair &q) { return make_pair(p.first - q.first, p.second - q.second); } template istream &operator>>(istream &is, pair &p) { S a; T b; is >> a >> b; p = make_pair(a, b); return is; } template ostream &operator<<(ostream &os, const pair &p) { return os << p.first << ' ' << p.second; } struct io_setup { io_setup() { ios_base::sync_with_stdio(false); cin.tie(NULL); cout << fixed << setprecision(15); } } io_setup; const int inf = (1 << 30) - 1; const ll INF = (1LL << 60) - 1; const int MOD = 1000000007; // const int MOD = 998244353; template struct Mod_Int { int x; Mod_Int() : x(0) {} Mod_Int(long long y) : x(y >= 0 ? y % mod : (mod - (-y) % mod) % mod) {} static int get_mod() { return mod; } Mod_Int &operator+=(const Mod_Int &p) { if ((x += p.x) >= mod) x -= mod; return *this; } Mod_Int &operator-=(const Mod_Int &p) { if ((x += mod - p.x) >= mod) x -= mod; return *this; } Mod_Int &operator*=(const Mod_Int &p) { x = (int)(1LL * x * p.x % mod); return *this; } Mod_Int &operator/=(const Mod_Int &p) { *this *= p.inverse(); return *this; } Mod_Int &operator++() { return *this += Mod_Int(1); } Mod_Int operator++(int) { Mod_Int tmp = *this; ++*this; return tmp; } Mod_Int &operator--() { return *this -= Mod_Int(1); } Mod_Int operator--(int) { Mod_Int tmp = *this; --*this; return tmp; } Mod_Int operator-() const { return Mod_Int(-x); } Mod_Int operator+(const Mod_Int &p) const { return Mod_Int(*this) += p; } Mod_Int operator-(const Mod_Int &p) const { return Mod_Int(*this) -= p; } Mod_Int operator*(const Mod_Int &p) const { return Mod_Int(*this) *= p; } Mod_Int operator/(const Mod_Int &p) const { return Mod_Int(*this) /= p; } bool operator==(const Mod_Int &p) const { return x == p.x; } bool operator!=(const Mod_Int &p) const { return x != p.x; } Mod_Int inverse() const { assert(*this != Mod_Int(0)); return pow(mod - 2); } Mod_Int pow(long long k) const { Mod_Int now = *this, ret = 1; for (; k > 0; k >>= 1, now *= now) { if (k & 1) ret *= now; } return ret; } friend ostream &operator<<(ostream &os, const Mod_Int &p) { return os << p.x; } friend istream &operator>>(istream &is, Mod_Int &p) { long long a; is >> a; p = Mod_Int(a); return is; } }; using mint = Mod_Int; template struct Combination { static vector _fac, _ifac; Combination() {} static void init(int n) { _fac.resize(n + 1), _ifac.resize(n + 1); _fac[0] = 1; for (int i = 1; i <= n; i++) _fac[i] = _fac[i - 1] * i; _ifac[n] = _fac[n].inverse(); for (int i = n; i >= 1; i--) _ifac[i - 1] = _ifac[i] * i; } static T fac(int k) { return _fac[k]; } static T ifac(int k) { return _ifac[k]; } static T inv(int k) { return fac(k - 1) * ifac(k); } static T P(int n, int k) { if (k < 0 || n < k) return 0; return fac(n) * ifac(n - k); } static T C(int n, int k) { if (k < 0 || n < k) return 0; return fac(n) * ifac(n - k) * ifac(k); } static T H(int n, int k) { // k 個の区別できない玉を n 個の区別できる箱に入れる場合の数 if (n < 0 || k < 0) return 0; return k == 0 ? 1 : C(n + k - 1, k); } static T second_stirling_number(int n, int k) { // n 個の区別できる玉を、k 個の区別しない箱に、各箱に 1 個以上玉が入るように入れる場合の数 T ret = 0; for (int i = 0; i <= k; i++) { T tmp = C(k, i) * T(i).pow(n); ret += ((k - i) & 1) ? -tmp : tmp; } return ret * ifac(k); } static T bell_number(int n, int k) { // n 個の区別できる玉を、k 個の区別しない箱に入れる場合の数 if (n == 0) return 1; k = min(k, n); vector pref(k + 1); pref[0] = 1; for (int i = 1; i <= k; i++) { if (i & 1) { pref[i] = pref[i - 1] - ifac(i); } else { pref[i] = pref[i - 1] + ifac(i); } } T ret = 0; for (int i = 1; i <= k; i++) ret += T(i).pow(n) * ifac(i) * pref[k - i]; return ret; } }; template vector Combination::_fac = vector(); template vector Combination::_ifac = vector(); using comb = Combination; int main() { int N, M; cin >> N >> M; vector cnt(N + 1, 0); vector P(N); rep(i, N) { cin >> P[i]; P[i]--; } vector used(N, false); rep(i, N) { if (used[i]) continue; int ptr = i, t = 0; while (!used[ptr]) { used[ptr] = true; ptr = P[ptr]; t++; } cnt[t]++; } mint ans = 1; comb::init(N); vector> pw(N + 1, vector(N + 1, 1)), ipw(N + 1, vector(N + 1, 1)); rep(i, N + 1) { rep(j, N) { pw[i][j + 1] = pw[i][j] * comb::fac(i); ipw[i][j + 1] = ipw[i][j] * comb::ifac(i); } } // print(cnt); rep2(i, 1, N) { int K = cnt[i]; if (K == 0) continue; vector dp(K + 1, 0), ndp(K + 1, 0); dp[0] = 1; mint tmp = 1; rep2(j, 1, K) { if (j > 1) tmp *= i; if (M % j != 0) continue; if (gcd(i, M / j) != 1) continue; ndp = dp; rep(t, K + 1) { if (dp[t] == 0) continue; mint coe = 1; for (int l = 1; l * j <= K - t; l++) { coe *= tmp; mint x = comb::P(K - t, l * j) * ipw[j][l] * comb::ifac(l) * pw[j - 1][l] * coe; ndp[t + l * j] += dp[t] * x; } } swap(dp, ndp); // cout << j << '\n'; // print(dp); } ans *= dp[K]; } cout << ans << '\n'; }