#include <iostream>
#include <algorithm>
#include <iomanip>
#include <vector>
#include <queue>
#include <deque>
#include <set>
#include <map>
#include <tuple>
#include <cmath>
#include <numeric>
#include <functional>
#include <cassert>

#define debug_value(x) cerr << "line" << __LINE__ << ":<" << __func__ << ">:" << #x << "=" << x << endl;
#define debug(x) cerr << "line" << __LINE__ << ":<" << __func__ << ">:" << x << endl;

template<class T> inline bool chmax(T& a, T b) { if (a < b) { a = b; return 1; } return 0; }
template<class T> inline bool chmin(T& a, T b) { if (a > b) { a = b; return 1; } return 0; }

using namespace std;
typedef long long ll;

template<typename T>
vector<vector<T>> vec2d(int n, int m, T v){
    return vector<vector<T>>(n, vector<T>(m, v));
}

template<typename T>
vector<vector<vector<T>>> vec3d(int n, int m, int k, T v){
    return vector<vector<vector<T>>>(n, vector<vector<T>>(m, vector<T>(k, v)));
}

template<typename T>
void print_vector(vector<T> v, char delimiter=' '){
    if(v.empty()) {
        cout << endl;
        return;
    }
    for(int i = 0; i+1 < v.size(); i++) cout << v[i] << delimiter;
    cout << v.back() << endl;
}

const ll MOD = 1000000007;

class ModInt{
    public:
    ll v;
    ModInt(ll _v = 0){
        if(_v < 0) _v = (_v%MOD)+MOD;
        if(_v >= MOD) _v %= MOD;
        v = _v;
    }
    ModInt operator+(ll n){
        return ModInt((v+n)%MOD);
    }
    ModInt operator-(ll n){
        return ModInt((v-n+MOD)%MOD);
    }
    ModInt operator*(ll n){
        if(n >= MOD) n %= MOD;
        return ModInt((v*n)%MOD);
    }
    ModInt operator/(ll n){
        return ModInt((ModInt(n).inv()*v).v%MOD);
    }

    ModInt &operator+=(ll n){
        v = (v+n)%MOD;
        return *this;
    }
    ModInt &operator-=(ll n){
        v = (v-n+MOD)%MOD;
        return *this;
    }
    ModInt &operator*=(ll n){
        v = (v*n+MOD)%MOD;
        return *this;
    }
    
    
    ModInt operator+(ModInt n){
        return ModInt((v+n.v)%MOD);
    }
    ModInt operator-(ModInt n){
        return ModInt((v-n.v+MOD)%MOD);
    }
    ModInt operator*(ModInt n){
        return ModInt((v*n.v)%MOD);
    }
    ModInt operator/(ModInt n){
        return ModInt((n.inv()*v).v%MOD);
    }

    ModInt &operator+=(ModInt n){
        v = (v+n.v)%MOD;
        return *this;
    }
    ModInt &operator-=(ModInt n){
        v = (v-n.v+MOD)%MOD;
        return *this;
    }
    ModInt &operator*=(ModInt n){
        v = (v*n.v)%MOD;
        return *this;
    }

    bool operator==(ModInt n){
        return v == n.v;
    }
    bool operator!=(ModInt n){
        return v != n.v;
    }
    ModInt &operator=(ll n){
        v = n%MOD;
        return *this;
    }

    ModInt inv(){
        if(v == 1) return ModInt(1);
        else return ModInt(MOD-ModInt(MOD%v).inv().v*(MOD/v)%MOD);
    }
};

ostream& operator<<(ostream& os, const ModInt& m){
    os << m.v;
    return os;
}

istream & operator >> (istream &in,  ModInt &m){
    in >> m.v;
    return in;
}

ModInt pow(ModInt a, ll n) {
    assert(n >= 0);
	ModInt ans = 1;
    while (n > 0) {
        if (n&1) ans = ans*a;
        a = a*a;
        n >>= 1;
    }
	return ans;
}

struct UnionFind {
    vector<int> data;
    UnionFind(int size) : data(size, -1) {}
    bool unionSet(int x, int y) {
        x = root(x); y = root(y);
        if (x != y) {
        if (data[y] < data[x]) swap(x, y);
        data[x] += data[y]; data[y] = x;
        }
        return x != y;
    }
    bool findSet(int x, int y) {
        return root(x) == root(y);
    }
    int root(int x) {
        return data[x] < 0 ? x : data[x] = root(data[x]);
    }
    int size(int x) {
        return -data[root(x)];
    }
};

#define N_MAX 200002
ModInt inv[N_MAX],fac[N_MAX],finv[N_MAX];

void init(){
    fac[0]=1;fac[1]=1;
    finv[0]=1;finv[1]=1;
    inv[1]=1;
    for(int i=2;i<N_MAX;i++){
        inv[i]=ModInt(MOD)-inv[MOD%i]*(MOD/i);
        fac[i]=fac[i-1]*(ll) i;
        finv[i]=finv[i-1]*inv[i];
    }
}

ModInt comb(ll n, ll r){
    if(n < r){
        return ModInt(0);
    }else{
        return fac[n]*finv[r]*finv[n-r];
    }
}

using mint = ModInt;

int naive(int n, int m, vector<int> a){
    vector<int> p(n);
    iota(p.begin(), p.end(), 0);
    auto ok = [&](vector<int> p){
        auto b = vector<int>(n);
        iota(b.begin(), b.end(), 0);
        for(int i = 0; i < m; i++){
            for(int j = 0; j < n; j++){
                b[j] = p[b[j]];
            }
        }
        for(int i = 0; i < n; i++){
            if(b[i] != a[i]) return false;
        }
        return true;
    };
    int ans = 0;
    do{
        if(ok(p)) {
            // print_vector(p);
            ans++;
        }
    }while(next_permutation(p.begin(), p.end()));
    return ans;
}

mint solve(int n, int m, vector<int> a){
    UnionFind uf(n);
    for(int i = 0; i < n; i++) {
        uf.unionSet(i, a[i]);
    }
    vector<int> cnt(n+1);
    for(int i = 0; i < n; i++){
        if(uf.root(i) != i) continue;
        cnt[uf.size(i)]++;
    }
    mint ans = 1;
    for(int x = 1; x <= n; x++) {
        if(cnt[x] == 0) continue;
        vector<mint> pattern(cnt[x]+1, 0);
        for(int c = 1; c <= cnt[x]; c++){
            int n_cycle = x*c;
            if(x == 1){
                if(m%n_cycle == 0) pattern[c] = fac[c-1].v;
                continue;
            }
            
            if(m%n_cycle != 0){
                int xx = m%n_cycle;
                // debug_value(xx)
                if(xx%c == 0){
                    int cc = xx/c;
                    if(gcd(cc, x) == 1) pattern[c] = 1;
                }
            }
            
        }
        auto dp = vec2d(cnt[x]+1, cnt[x]+1, mint(0));
        // cout << x << ':';
        // print_vector(pattern);
        dp[0][0] = 1;
        for(int c = 1; c <= cnt[x]; c++){
            if(c >= 2){
                pattern[c] *= pow(mint(x), c-1);
            }
            for(int j = 0; j <= cnt[x]; j++){
                mint select = 1;
                int rem = cnt[x]-j;
                for(int k = 0; j+k*c <= cnt[x]; k++){
                    if(k > 0) select *= comb(rem, c)*pattern[c];
                    dp[c][j+k*c] += dp[c-1][j]*select*finv[k]; 
                    if(k > 0) rem -= c;
                }
            }
            // print_vector(dp[c]);
        }
        // debug_value(cnt[x])
        // debug_value(dp[cnt[x]][cnt[x]])
        ans *= dp[cnt[x]][cnt[x]];
    }
    return ans;
}

int main(){
    ios::sync_with_stdio(false);
    cin.tie(0);
    cout << setprecision(10) << fixed;
    init();
    int n, m; cin >> n >> m;
    vector<int> a(n);
    for(int i = 0; i < n; i++) {
        cin >> a[i]; a[i]--;
    }
    cout << solve(n, m, a) << endl;
    // cout << naive(n, m, a) << endl;
    // iota(a.begin(), a.end(), 0);
    // do{ 
    //     if(solve(n, m, a).v != naive(n, m, a)) print_vector(a);
    // }while(next_permutation(a.begin(), a.end()));
}