#pragma GCC optimization ("O3")

#include <bits/stdc++.h>

using namespace std;

using ll = long long;
using vec = vector<ll>;
using mat = vector<vec>;
using pll = pair<ll,ll>;
using dvec = vector<double>;
using dmat = vector<dvec>;

#define INF (1LL<<61)
//#define MOD 1000000007LL 
#define MOD 998244353LL
#define EPS (1e-10)

#define PR(x) cout << (x) << endl
#define PS(x) cout << (x) << " "
#define REP(i,m,n) for(ll (i)=(m),(i_len)=(n);(i)<(i_len);++(i))
#define FORE(i,v) for(auto (i):v)
#define ALL(x) (x).begin(), (x).end()
#define SZ(x) ((ll)(x).size())
#define REV(x) reverse(ALL((x)))
#define ASC(x) sort(ALL((x)))
#define DESC(x) {ASC((x)); REV((x));}
#define BIT(s,i) (((s)>>(i))&1)
#define pb push_back
#define fi first
#define se second

template<class T> inline int chmin(T& a, T b) {if(a>b) {a=b; return 1;} return 0;}
template<class T> inline int chmax(T& a, T b) {if(a<b) {a=b; return 1;} return 0;}
class mint {
public:
    ll x;
    mint(ll x=0) : x((x%MOD+MOD)%MOD) {}
    mint operator-() const {return mint(-x);}
    mint& operator+=(const mint& a) {if((x+=a.x)>=MOD) x-=MOD; return *this;}
    mint& operator-=(const mint& a) {if((x+=MOD-a.x)>=MOD) x-=MOD; return *this;}
    mint& operator*=(const mint& a) {(x*=a.x)%=MOD; return *this;}
    mint operator+(const mint& a) const {mint b(*this); return b+=a;}
    mint operator-(const mint& a) const {mint b(*this); return b-=a;}
    mint operator*(const mint& a) const {mint b(*this); return b*=a;}
    mint pow(ll t) const {if(!t) return 1; mint a=pow(t>>1); return (t&1?*this*a:a)*a;}
    mint inv() const {return pow(MOD-2);}
    mint& operator/=(const mint& a) {return *this*=a.inv();}
    mint operator/(const mint& a) const {mint b(*this); return b/=a;}
};
istream &operator>>(istream& is, mint& a) {ll t; is>>t; a=t; return is;}
ostream &operator<<(ostream& os, const mint& a) {return os<<a.x;}
using mvec = vector<mint>;
using mmat = vector<mvec>;

struct UnionFind {
    
    vec par;
    vec rank;
    vec num;
    
    UnionFind(ll N) {
        par = vec(N);
        REP(i,0,N) par[i] = i;
        rank = vec(N, 0);
        num = vec(N, 1);
    }

    ll root(ll x) {
        if(par[x] == x) return x;
        return par[x] = root(par[x]);
    } 

    void unite(ll x, ll y) {
        ll rx = root(x);
        ll ry = root(y);
        if(rx == ry) return;
        if(rank[rx] < rank[ry]) swap(rx, ry);
        par[ry] = rx;
        num[rx] += num[ry];
        if(rank[rx] == rank[ry]) ++rank[rx];
    }

    bool same(ll x, ll y) {
        return root(x) == root(y);
    }

    ll size(ll x) {
        return num[root(x)];
    }

};

int main()
{
    ll N, M;
    cin >> N >> M;
    UnionFind uf(N);
    REP(i,0,N) {
        ll p;
        cin >> p;
        uf.unite(p-1, i);
    }

    map<ll,ll> C;
    REP(i,0,N) C[uf.root(i)] = uf.size(uf.root(i));
    mvec F(M+1);
    F[0] = mint(1);
    REP(i,1,M+1) F[i] = mint(i)*F[i-1];

    mint ans;
    REP(i,0,M+1) {
        mint tmp(1);
        FORE(c,C) tmp *= mint(M-i-1).pow(c.se)+mint(-1).pow(c.se)*mint(M-i-1);
        ans += mint(i%2?-1:1)*F[M]*F[M-i].inv()*F[i].inv()*tmp;
    }
    ans /= F[M];
    PR(ans.x);

    return 0;  
}

/*



*/