#include <bits/stdc++.h>
using namespace std;
const long long MOD = 998244353;
long long modpow(long long a, long long b){
	long long ans = 1;
	while (b > 0){
		if (b % 2 == 1){
			ans *= a;
			ans %= MOD;
		}
		a *= a;
		a %= MOD;
		b /= 2;
	}
	return ans;
}
long long modinv(long long a){
	return modpow(a, MOD - 2);
}
vector<long long> mf = {1};
vector<long long> mfi = {1};
long long modfact(int n){
	if (mf.size() > n){
		return mf[n];
	} else {
		for (int i = mf.size(); i <= n; i++){
			long long next = mf.back() * i % MOD;
			mf.push_back(next);
			mfi.push_back(modinv(next));
		}
		return mf[n];
	}
}
long long modfactinv(int n){
	if (mfi.size() > n){
		return mfi[n];
	} else {
		return modinv(modfact(n));
	}
}
long long modbinom(int n, int k){
	if (n < 0 || k < 0 || k > n){
		return 0;
	} else {
		return modfact(n) * modfactinv(k) % MOD * modfactinv(n - k) % MOD;
	}
}
vector<vector<long long>> matmul(vector<vector<long long>> A, vector<vector<long long>> B){
	int N = A.size();
	vector<vector<long long>> ans(N, vector<long long>(N, 0));
	for (int i = 0; i < N; i++){
		for (int j = 0; j < N; j++){
			for (int k = 0; k < N; k++){
				ans[i][k] += A[i][j] * B[j][k] % MOD;
				ans[i][k] %= MOD;
			}
		}
	}
	return ans;
}
vector<vector<long long>> matexp(vector<vector<long long>> A, long long b){
	int N = A.size();
	vector<vector<long long>> ans(N, vector<long long>(N, 0));
	for (int i = 0; i < N; i++){
		ans[i][i] = 1;
	}
	while (b > 0){
		if (b % 2 == 1){
			ans = matmul(ans, A);
		}
		A = matmul(A, A);
		b /= 2;
	}
	return ans;
}
int main(){
  int N, M;
  cin >> N >> M;
  vector<int> P(N);
  for (int i = 0; i < N; i++){
    cin >> P[i];
    P[i]--;
  }
  vector<int> s;
  vector<bool> used(N, false);
  for (int i = 0; i < N; i++){
    if (!used[i]){
      int cnt = 0;
      for (int j = i; !used[j]; j = P[j]){
        used[j] = true;
        cnt++;
      }
      s.push_back(cnt);
    }
  }
  int cnt = s.size();
  long long ans = 0;
  for (int i = M; i >= 2; i--){
    long long add = 1;
    unordered_map<int, long long> mp;
    for (int j = 0; j < cnt; j++){
      if (!mp.count(s[j])){
        vector<vector<long long>> mat(2, vector<long long>(2));
        mat[0][0] = 0;
        mat[0][1] = i - 1;
        mat[1][0] = 1;
        mat[1][1] = i - 2;
        mat = matexp(mat, s[j]);
        mp[s[j]] = mat[0][0] * i % MOD;
      }
      add *= mp[s[j]];
      add %= MOD;
    }
    add *= modbinom(M, i);
    add %= MOD;
    if ((M - i) % 2 == 1){
      add = (MOD - add) % MOD;
    }
    ans += add;
    ans %= MOD;
  }
  ans *= modfactinv(M);
  ans %= MOD;
  cout << ans << endl;
}