#include <iostream>

using namespace std;
using ll = long long;
const int MX = 100010;
ll f[MX],inv[MX],fi[MX];
constexpr ll mod = 998244353;
void solve(){
    inv[1] = 1;
    for(int i=2;i<MX;i++){
        inv[i] = mod - (mod/i)*inv[mod%i]%mod;
    }
    f[0] = fi[0] = 1;
    for(int i=1;i<MX;i++){
        f[i] = f[i-1]*i%mod;
        fi[i] = fi[i-1]*inv[i]%mod;
    }
}

ll nck(ll n, ll k){
    if(n<0 || k<0 || n<k) return 0;
    return f[n]*fi[k]%mod*fi[n-k]%mod;
}

ll beki[5010][5010];
int par[100010],sz[100010];
void init(int n){
	for(int i=0;i<n;i++) par[i] = i,sz[i] = 1;
}

int find(int x){
	if(par[x]==x) return x;
	return par[x] = find(par[x]);
}

void unite(int x, int y){
	x = find(x); y = find(y);
	if(x==y) return;
	if(sz[x]>sz[y]) swap(x,y);
	par[x] = y; sz[y] += sz[x];
}

bool same(int x, int y){
	return find(x)==find(y);
}

int main(){
    ll i,j,n,m; cin >> n >> m;
    init(n);
    for(i=0;i<n;i++){
        int x; cin >> x; x--;
        unite(i,x);
    }
    for(i=0;i<=5000;i++){
        beki[i][0] = 1;
        for(j=1;j<=5000;j++) beki[i][j] = (beki[i][j - 1])*i%mod;
    }
    solve();
    ll ans = 0;
    for(i=2;i<=m;i++){
        ll s = 1;
        for(j=0;j<n;j++){
            if(find(j)!=j) continue;
            ll k = 1;
            if(sz[j]&1) k = mod - 1;
            (s *= (beki[i - 1][sz[j]] + (i - 1)*k%mod)%mod) %= mod;
        }
        (s *= nck(m,i)) %= mod;
        if((m - i)&1) (ans += mod - s) %= mod;
        else (ans += s) %= mod;
    }
    cout << ans*fi[m]%mod << endl;
}