#include<bits/stdc++.h>
namespace {
#pragma GCC diagnostic push
#pragma GCC diagnostic ignored "-Wunused-function"
#include<atcoder/all>
#pragma GCC diagnostic pop
using namespace std;
using namespace atcoder;
#define rep(i,n) for(int i = 0; i < (int)(n); i++)
#define rrep(i,n) for(int i = (int)(n) - 1; i >= 0; i--)
#define all(x) begin(x), end(x)
#define rall(x) rbegin(x), rend(x)
template<class T> bool chmax(T& a, const T& b) { if (a < b) { a = b; return true; } else return false; }
template<class T> bool chmin(T& a, const T& b) { if (b < a) { a = b; return true; } else return false; }
using ll = long long;
using P = pair<int,int>;
using VI = vector<int>;
using VVI = vector<VI>;
using VL = vector<ll>;
using VVL = vector<VL>;
using mint = modint1000000007;

VI cycle_decomposition(const vector<int>& a) {
  const int n = a.size();
  vector<char> visited(n);
  VI res;
  for(int i = 0; i < n; i++) if (!visited[i]) {
    int cnt = 0;
    int v = i;
    do {
      visited[v] = true;
      cnt++;
      v = a[v];
    } while (v != i);
    res.emplace_back(cnt);
  }
  return res;
}


constexpr int FACT_SIZE = 1000000;
mint Fact[FACT_SIZE + 1];
mint iFact[FACT_SIZE + 1];
const auto fact_init = [] {
    Fact[0] = mint::raw(1);
    for(int i = 1; i <= FACT_SIZE; ++i) {
        Fact[i] = Fact[i-1] * i;
    }
    iFact[FACT_SIZE] = Fact[FACT_SIZE].inv();
    for(int i = FACT_SIZE; i; --i) {
        iFact[i-1] = iFact[i] * i;
    }
    return false;
}();

mint comb(int n, int k) {
    if (k == 0) return mint::raw(1);
    assert(n >= 0 && k >= 0);
    if (k > n) return mint::raw(0);
    return Fact[n] * iFact[n - k] * iFact[k];
}

mint icomb(int n, int k) {
    return iFact[n] * Fact[n - k] * Fact[k];
}

mint fact(int n) {return Fact[n];}
mint perm(int n, int k) {
    assert(0 <= n);
    return Fact[n] * iFact[n - k];
}

} int main() {
  ios::sync_with_stdio(false);
  cin.tie(0);
  int n, m;
  cin >> n >> m;
  VI a(n);
  rep(i, n) cin >> a[i], a[i]--;
  auto cs = cycle_decomposition(a);
  sort(all(cs));
  mint ans = 1;
  int sz = cs.size();
  for(int i = 0; i < sz;) {
    int j = i + 1;
    while(j < sz && cs[i] == cs[j]) j++;
    int cnt = j - i;
    int len = cs[i];
    vector<pair<int, mint>> d;
    for(int i = 1; i <= cnt; i++) if (m % (i * len) == i % (i * len)) {
      d.emplace_back(i, mint(len).pow(i - 1));
    }
    vector<mint> dp(cnt + 1);
    dp[0] = Fact[cnt];
    rep(i, cnt) {
      dp[i] /= cnt - i;
      for(auto [j, v]: d) {
        if (i + j > cnt) break;
        dp[i + j] += dp[i] * v;
      }
    }
    ans *= dp[cnt];
    i = j;
  }
  cout << ans.val() << '\n';
}