/**
 *   @FileName	a.cpp
 *   @Author	kanpurin
 *   @Created	2021.02.12 23:24:38
**/

#include "bits/stdc++.h" 
using namespace std; 
typedef long long ll;


class UnionFind {
private:
    vector<int> par;
public:
    UnionFind(int n) {
        par.resize(n, -1);
    }
    int root(int x) {
        if (par[x] < 0) return x;
        return par[x] = root(par[x]);
    }
    bool unite(int x, int y) {
        int rx = root(x);
        int ry = root(y);
        if (rx == ry) return false;
        if (size(rx) < size(ry)) swap(rx, ry);
        par[rx] += par[ry];
        par[ry] = rx;
        return true;
    }
    bool same(int x, int y) {
        int rx = root(x);
        int ry = root(y);
        return rx == ry;
    }
    int size(int x) {
        return -par[root(x)];
    }
};
template< int MOD >
struct mint {
public:
    long long x;
    mint(long long x = 0) :x((x%MOD+MOD)%MOD) {}
    mint(std::string &s) {
        long long z = 0;
        for (int i = 0; i < s.size(); i++) {
            z *= 10;
            z += s[i] - '0';
            z %= MOD;
        }
        this->x = z;
    }
    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) {
        long long n = MOD - 2;
        mint u = 1, b = a;
        while (n > 0) {
            if (n & 1) {
                u *= b;
            }
            b *= b;
            n >>= 1;
        }
        return *this *= u;
    }
    mint operator+(const mint &a) const {
        mint res(*this);
        return res += a;
    }
    mint operator-() const {return mint() -= *this; }
    mint operator-(const mint &a) const {
        mint res(*this);
        return res -= a;
    }
    mint operator*(const mint &a) const {
        mint res(*this);
        return res *= a;
    }
    mint operator/(const mint &a) const {
        mint res(*this);
        return res /= a;
    }
    friend std::ostream& operator<<(std::ostream &os, const mint &n) {
        return os << n.x;
    }
    friend std::istream &operator>>(std::istream &is, mint &n) {
        long long x;
        is >> x;
        n = mint(x);
        return is;
    }
    bool operator==(const mint &a) const {
        return this->x == a.x;
    }
    bool operator!=(const mint &a) const {
        return this->x != a.x;
    }
    mint pow(long long k) const {
        mint ret = 1;
        mint p = this->x;
        while (k > 0) {
            if (k & 1) {
                ret *= p;
            }
            p *= p;
            k >>= 1;
        }
        return ret;
    }
};
constexpr int MOD = 998244353;

template<typename T>
struct Combination {
private:
    int N;
public:
    vector< T > FACT, IFACT;
    
    Combination(int n) : N(n) {
        FACT.resize(n + 1);
        IFACT.resize(n + 1);
        FACT[0] = 1;
        for (int i = 1; i <= n; i++) {
            FACT[i] = FACT[i - 1] * i;
        }
        IFACT[n] = T(1) / FACT[n];
        for (int i = n-1; i >= 0; i--) {
            IFACT[i] = IFACT[i+1] * (i+1);
        }
    }
    T comb(int n, int r) {
        if (n < 0 || r < 0 || r > n) return 0;
        if (r > n / 2) r = n - r;
        return FACT[n] * IFACT[n - r] * IFACT[r];
    }
};
int main() {
    int n,m;cin >> n >> m;
    UnionFind uf(n);
    Combination<mint<MOD>> cb(m);
    for (int i = 0; i < n; i++) {
        int p;cin >> p;
        uf.unite(p-1,i);
    }
    vector<vector<mint<MOD>>> f(n+1,vector<mint<MOD>>(m+1));
    for (int i = 0; i < n-1; i++) {
        if (i == 0) {
            for (int j = 0; j < m-1; j++) {
                f[i+2][j+2] = mint<MOD>(j+2)*(j+1);
            }
        }
        else {
            for (int j = 0; j < m-1; j++) {
                f[i+2][j+2] = f[i+1][j+2]*j+f[i][j+2]*(j+1);
            }
        }
    }
    vector<int> c;
    for (int i = 0; i < n; i++) {
        if (uf.root(i) == i) {
            c.push_back(uf.size(i));
        }
    }
    mint<MOD> ans = 0;
    for (int i = 0; i <= m; i++) {
        mint<MOD> total = 1;
        for (int j = 0; j < c.size(); j++) {
            total *= f[c[j]][i];
        }
        if ((i & 1) == (m & 1)) {
            ans += total * cb.comb(m,i);
        }
        else {
            ans -= total * cb.comb(m,i);
        }
    }
    cout << ans * cb.IFACT[m] << endl;
    return 0;
}