#include <iostream>
#include <vector>
#include <string>
#include <algorithm>
#include <cstdio>
#include <cstring>
#include <cmath>
using namespace std;
using ll = long long;

constexpr int P = 998244353;

ll powmod(ll n, ll k) {
    ll r = 1, t = n % P;
    for (; k != 0; k /= 2) {
        if (k & 1) r = r * t % P;
        t = t * t % P;
    }
    return r;
}
ll modinv(ll n) {
    return powmod(n, P - 2);
}

vector<int> f0, f1;
void init(int n) {
    f0.resize(n + 1);
    f0[0] = 1;
    for (int i = 1; i <= n; i++) {
        f0[i] = (ll)f0[i - 1] * i % P;
    }
    f1.resize(n + 1);
    f1[n] = modinv(f0[n]);
    for (int i = n; i > 0; i--) {
        f1[i - 1] = (ll)f1[i] * i % P;
    }
}
ll fact(int k) {
    return f0[k];
}
ll comb(int n, int k) {
    if (n < k || k < 0) return 0;
    return (ll)f0[n] * f1[k] % P * f1[n - k] % P;
}

int main() {
    ios::sync_with_stdio(false);
    cin.tie(0);

    int n, m;
    cin >> n >> m;

    vector<int> p(n);
    for (int i = 0; i < n; i++) {
        cin >> p[i];
        p[i]--;
    }

    vector<int> q(n, 0), u;
    for (int i = 0; i < n; i++) {
        if (q[i]) continue;
        int k = 1;
        q[i] = 1;
        for (int j = p[i]; j != i; j = p[j]) {
            k++;
            q[j] = 1;
        }
        u.push_back(k);
    }

    init(n);

    vector<int> y(m + 1);
    for (int i = 1; i <= m; i++) {
        y[i] = powmod(i, u.size());
    }

    auto f = [&](int n) {
        if (n < m) return 0LL;
        ll r = 0;
        for (int i = 1; i <= m; i++) {
            r += y[i] * comb(m, i) % P * ((m - i) % 2 == 0 ? 1 : -1);
        }
        r %= P;
        if (r < 0) r += P;

        r = r * f1[m] % P;

        return r;
    };

    vector<int> dp(n, 0);
    dp[0] = 1;
    for (int k : u) {
        for (int i = n; --i >= 0;) {
            ll t = 0;
            for (int j = 0; j < k && j <= i; j++) {
                t += (ll)dp[i - j] * (j == k - 1 ? 1 : comb(k, j)) % P;
            }
            dp[i] = t % P;
        }
    }

    ll r = 0;
    for (int i = (int)u.size(); i <= n; i++) {
        r += f(i) * dp[n - i] % P * ((n - i) % 2 == 0 ? 1 : -1);
        for (int i = 1; i <= m; i++) {
            y[i] = (ll)y[i] * i % P;
        }
    }
    r %= P;
    if (r < 0) r += P;

    cout << r << endl;

    return 0;
}