#line 2 "/home/defineprogram/Desktop/Library/template/template.cpp"
#include <bits/stdc++.h>
using namespace std;
#define ll long long
#define rep(i, n) for (int i = 0; i < n; i++)
#define REP(i, n) for (int i = 1; i < n; i++)
#define rev(i, n) for (int i = n - 1; i >= 0; i--)
#define REV(i, n) for (int i = n - 1; i > 0; i--)
#define all(v) v.begin(), v.end()
#define PL pair<ll, ll>
#define PI pair<int,int>
#define len(s) (int)s.size()

template <class T, class U>
inline bool chmin(T &a, U b) {
    if (a > b) {
        a = b;
        return true;
    }
    return false;
}
template <class T, class U>
inline bool chmax(T &a, U b) {
    if (a < b) {
        a = b;
        return true;
    }
    return false;
}
constexpr ll inf = 3e18;
#line 3 "/home/defineprogram/Desktop/Library/math/extgcd.cpp"

ll extGCD(ll a, ll b, ll &x, ll &y) {
    if (!b) {
        x = 1;
        y = 0;
        return a;
    }
    ll d = extGCD(b, a % b, y, x);
    y -= a / b * x;
    return d;
}

ll modinv(ll a, ll m) {
    ll x, y;
    extGCD(a, m, x, y);
    return (x % m + m) % m;
}
#line 4 "/home/defineprogram/Desktop/Library/math/modint.cpp"

template <int MOD>
struct mint {
    int32_t n;
    mint() : n(0) {}
    mint(ll x) : n(x >= 0 ? x % MOD : (MOD - (-x) % MOD) % MOD) {}

    mint &operator+=(const mint &p) {
        if ((n += p.n) >= MOD) n -= MOD;
        return *this;
    }
    mint &operator-=(const mint &p) {
        if ((n += MOD - p.n) >= MOD) n -= MOD;
        return *this;
    }
    mint &operator*=(const mint &p) {
        n = 1ll * n * p.n % MOD;
        return *this;
    }
    mint &operator/=(const mint &p) {
        *this *= p.inverse();
        return *this;
    }
    mint operator-() const { return mint(-n); }
    mint operator+(const mint &p) const { return mint(*this) += p; }
    mint operator-(const mint &p) const { return mint(*this) -= p; }
    mint operator*(const mint &p) const { return mint(*this) *= p; }
    mint operator/(const mint &p) const { return mint(*this) /= p; }
    bool operator==(const mint &p) const { return n == p.n; }
    bool operator!=(const mint &p) const { return n != p.n; }

    friend ostream &operator<<(ostream &os, const mint &p) {
        return os << p.n;
    }
    friend istream &operator>>(istream &is, mint &p) {
        int x;
        is >> x;
        p = mint(x);
        return is;
    }
    mint pow(int64_t x) const {
        mint res(1), mul(n);
        while (x > 0) {
            if (x & 1) res *= mul;
            mul *= mul;
            x >>= 1;
        }
        return res;
    }
    mint inverse() const {
        return mint(modinv(n,MOD));
    }
};
/*
@brief mod int
@docs docs/modint.md
*/
#line 3 "main.cpp"
constexpr int mod=998244353;
using modint=mint<mod>;

#line 3 "/home/defineprogram/Desktop/Library/math/Combination.cpp"

template <int MOD>
struct Combination {
    using modint = mint<MOD>;
    vector<modint> perm, inv;

    Combination(int x = 1e6) {
        perm.resize(x);
        inv.resize(x);
        perm[0] = modint(1);
        REP(i, x + 1)
        perm[i] = perm[i - 1] * i;
        inv[x] = perm[x].pow(MOD - 2);
        for (int i = x - 1; i >= 0; i--) {
            inv[i] = inv[i + 1] * (i + 1);
        }
    }
    modint nCk(int x, int y) {
        if (x < y) return modint(0);
        return perm[x] * inv[x - y] * inv[y];
    }
};
/*
@brief Combination (nCk)
@docs docs/Combination.md
*/
#line 7 "main.cpp"

Combination<mod> C;

int N,M;
int P[5005];
bool used[5005];
int main() {
    cin.tie(0); ios::sync_with_stdio(false);
    cin>>N>>M;
    rep(i,N){
        cin>>P[i];P[i]--;
    }
    modint ans=0;
    for(int i=2;i<=M;i++){
        modint tapi=1;
        memset(used,false,sizeof(used));
        rep(j,N)if(!used[j]){
            int cur=j;
            int cnt=0;
            do{
                used[cur]=true;
                cnt++;
                cur=P[cur];
            }while(cur!=j);

            modint dp[2],dp2[2];
            dp[0]=i;
            rep(k,cnt-2){
                swap(dp,dp2);
                dp[0]=dp[1]=0;
                dp[0]+=dp2[1];
                dp[1]+=dp2[0]*(i-1);
                dp[1]+=dp2[1]*(i-2);
            }
            modint res=dp[0]*(i-1)+dp[1]*(i-2);
            tapi*=res;
        }
        if((M-i)%2==0)ans+=C.nCk(M,i)*tapi;
        else ans-=C.nCk(M,i)*tapi;
    }
    REP(i,M+1)ans/=i;
    cout<<ans<<"\n";
}