#include <bits/stdc++.h>
#include <numeric>
using namespace std;

// using mint = long double;
// using mint = modint998244353;
// using mint = modint1000000007;

typedef long long ll;
typedef pair<ll, ll> P;
typedef pair<P, ll> T;
typedef pair<ll, vector<ll> > Pd;

const ll INF = 1e18;
const ll fact_table = 3200008;

priority_queue <ll> pql;
priority_queue <P> pqp;
//big priority queue
// priority_queue <ll, vector<ll>, greater<ll> > pqls;
priority_queue <P, vector<P>, greater<P> > pqps;
//small priority queue
//top pop

ll dx[8] = {1, 0, -1, 0, 1, 1, -1, -1};
ll dy[8] = {0, 1, 0, -1, -1, 1, 1, -1};
//↓,→,↑,←

/*
#define endl "\n"
#ifdef ENJAPMA
#undef endl
#endif
*/

#define p(x) cout<<x<<endl;
#define el cout<<endl;
#define pe(x) cout<<x<<" ";
#define ps(x) cout<<fixed<<setprecision(25)<<x<<endl;
#define pu(x) cout<<(x);
#define pb push_back
#define lb lower_bound
#define ub upper_bound
#define pc(x) cout << x << ",";
#define rep(i, n) for (ll i = 0; i < (n); i ++)
#define rep2(i, a, b) for (ll i = a; i <= (b); i++)
#define rep3(i, a, b) for (ll i = a; i >= (b); i--)

typedef vector<ll> vec;
typedef vector<vector<ll>> mat;

// vec v(n) -> 長さnのベクトルを宣言
// mat dp(h, vec(w)) -> h * w の行列を宣言

const ll mod = 998244353ll;
// const ll mod = 1000000007ll;

ll mypow(ll a, ll b, ll m = mod) {ll x = 1; while (b) {while (!(b & 1)) {(a *= a) %= m; b >>= 1;}(x *= a) %= m; b--;} return x;}
vec rv(ll read) { vec res(read); for (int i = 0; i < read; i++) { cin >> res[i]; } return res;}
void YES(bool cond) { if (cond) { p("YES");} else { p("NO");} return;}
void Yes(bool cond) { if (cond) { p("Yes");} else { p("No");} return;}
void line() { p("--------------------"); return;}


ll fact[fact_table + 5], rfact[fact_table + 5];

void c3_init() {
    fact[0] = rfact[0] = 1;
    for (ll i = 1; i <= fact_table; i++) {
        fact[i] = (fact[i - 1] * i) % mod;
    }
    rfact[fact_table] = mypow(fact[fact_table], mod - 2, mod);
    for (ll i = fact_table; i >= 1; i--) {
        rfact[i - 1] = rfact[i] * i;
        rfact[i - 1] %= mod;
    }
    return;
}
ll c3(ll n, ll r) {
    return (((fact[n] * rfact[r]) % mod ) * rfact[n - r]) % mod;
}


bool icpc = false;
bool multicase = false;

ll n, m;
ll p[5005];
ll x[5005];
bool used[5005][5005];
ll dp[5005][5005][3];

ll dfs(ll color, ll i, ll par) {

    if (used[color][i]) {
        // 清算を行う
        return dp[color][par][0];
    }
    used[color][i] = true;

    if (par == -1) {
        dp[color][i][0] = 0;
        dp[color][i][1] = color;
    } else {
        dp[color][i][1] += dp[color][par][0];

        dp[color][i][0] += dp[color][par][1] * (color - 1) % mod;
        dp[color][i][0] += dp[color][par][0] * (color - 2) % mod;

        dp[color][i][0] %= mod;
    }
    return dfs(color, p[i], i);
}

bool solve() {
    cin >> n >> m;
    c3_init();
    for (int i = 1; i <= n; i++) {
        cin >> p[i];
    }

    for (int color = 1; color <= m; color ++) {
        ll res = 1ll;
        for (int i = 1; i <= n; i++) {
            if (!used[color][i]) {
                res *= dfs(color, i, -1);
                res %= mod;
            }
        }
        x[color] = res;
    }

    ll ans = 0ll;
    ll flag = 1ll;
    for (int color = m; color >= 1; color --) {
        ans += ((x[color] * flag) % mod) * c3(m, color) % mod;
        flag = (mod - flag);
        ans %= mod;
    }
    ans *= rfact[m];
    ans %= mod;
    p(ans);

    return true;
}

int main() {

    ios::sync_with_stdio(false);
    cin.tie(nullptr);

    if (icpc) {
        while (solve());
        return 0;
    }
    ll q, testcase = 1;
    if (multicase) {
        cin >> q;
    } else {
        q = 1;
    }
    while (q--) {
        // pu("Case ");pu("#");pu(testcase);pu(": ");
        solve();
        testcase++;
    }

// solve();
    return 0;
}