#line 2 "lib/prelude.hpp"
#include <bits/stdc++.h>
using namespace std;
using ll = long long;
#define rep2(i, m, n) for (auto i = (m); i < (n); i++)
#define rep(i, n) rep2(i, 0, n)
#define repr2(i, m, n) for (auto i = (n); i-- > (m);)
#define repr(i, n) repr2(i, 0, n)
#define all(x) begin(x), end(x)
#line 2 "main.cpp"
#include <atcoder/convolution>
using mint = atcoder::modint1000000007;

vector<mint> conv(vector<mint> a, vector<mint> b, int deg = -1) {
  if (~deg)
    a.resize(min<int>(a.size(), deg)),
      b.resize(min<int>(b.size(), deg));
  auto f = convolution(a, b);
  if (~deg) f.resize(deg);
  return f;
}

vector<mint> exp(vector<mint> h, int deg) {
  assert(h[0] == 0);
  int n = 1 << atcoder::internal::ceil_pow2(deg);
  h.resize(n);
  vector<mint> f = {1}, g = {1};
  vector<mint> q(h.size() - 1);
  rep(i, q.size()) q[i] = h[i + 1] * (i + 1);
  for (int m = 1; m < n; m *= 2) {
    auto fgg = conv(conv(f, g, m), g, m);
    g.resize(m);
    rep(i, m) g[i] = g[i] * 2 - fgg[i];
    auto fq = conv(f, {q.begin(), q.begin() + m - 1});
    rep(i, fq.size()) fq[i] =
      -fq[i] + (i < f.size() - 1 ? f[i + 1] * (i + 1) : 0);
    auto w = conv(g, fq, m * 2 - 1);
    rep(i, m - 1) w[i] += q[i];
    w.push_back(0);
    repr(i, m * 2 - 1) w[i + 1] = h[i + 1] - w[i] / (i + 1);
    w[0] = h[0];
    auto fw = conv(f, w, m * 2);
    f.resize(m * 2);
    rep(i, m * 2) f[i] += fw[i];
  }
  return f;
}

int N, M, A[1000];
bool used[1000];
int cycles[1001];

int main() {
  scanf("%d%d", &N, &M);
  rep(i, N) scanf("%d", A+i), A[i]--;

  rep(i, N) if (!used[i]) {
    int cnt = 0;
    for (int v = i; !used[v]; v = A[v])
      used[v] = true, cnt++;
    cycles[cnt]++;
  }

  mint ans = 1;
  rep(m, N+1) if (cycles[m] != 0) {
    int l = cycles[m];
    vector<mint> poly(l+1);
    rep2(k, 1, l+1) if (M % k == 0 && gcd(M / k, m) == 1) {
      poly[k] = mint(m).pow(k-1) / k;
    }
    ans *= exp(move(poly), l+1)[l];
    rep(i, l) ans *= i+1;
  }

  printf("%d\n", ans.val());
}