#define LOCAL
#include <bits/stdc++.h>
using namespace std;
#pragma region Macros
typedef long long ll;
typedef __int128_t i128;
typedef unsigned int uint;
typedef unsigned long long ull;
#define ALL(x) (x).begin(), (x).end()

template <typename T> istream& operator>>(istream& is, vector<T>& v) {
    for (T& x : v) is >> x;
    return is;
}
template <typename T> ostream& operator<<(ostream& os, const vector<T>& v) {
    for (int i = 0; i < (int)v.size(); i++) {
        os << v[i] << (i + 1 == (int)v.size() ? "" : " ");
    }
    return os;
}
template <typename T, typename U> ostream& operator<<(ostream& os, const pair<T, U>& p) {
    os << '(' << p.first << ',' << p.second << ')';
    return os;
}
template <typename T, typename U, typename V> ostream& operator<<(ostream& os, const tuple<T, U, V>& t) {
    os << '(' << get<0>(t) << ',' << get<1>(t) << ',' << get<2>(t) << ')';
    return os;
}
template <typename T, typename U, typename V, typename W> ostream& operator<<(ostream& os, const tuple<T, U, V, W>& t) {
    os << '(' << get<0>(t) << ',' << get<1>(t) << ',' << get<2>(t) << ',' << get<3>(t) << ')';
    return os;
}
template <typename T, typename U> ostream& operator<<(ostream& os, const map<T, U>& m) {
    os << '{';
    for (auto itr = m.begin(); itr != m.end();) {
        os << '(' << itr->first << ',' << itr->second << ')';
        if (++itr != m.end()) os << ',';
    }
    os << '}';
    return os;
}
template <typename T, typename U> ostream& operator<<(ostream& os, const unordered_map<T, U>& m) {
    os << '{';
    for (auto itr = m.begin(); itr != m.end();) {
        os << '(' << itr->first << ',' << itr->second << ')';
        if (++itr != m.end()) os << ',';
    }
    os << '}';
    return os;
}
template <typename T> ostream& operator<<(ostream& os, const set<T>& s) {
    os << '{';
    for (auto itr = s.begin(); itr != s.end();) {
        os << *itr;
        if (++itr != s.end()) os << ',';
    }
    os << '}';
    return os;
}
template <typename T> ostream& operator<<(ostream& os, const multiset<T>& s) {
    os << '{';
    for (auto itr = s.begin(); itr != s.end();) {
        os << *itr;
        if (++itr != s.end()) os << ',';
    }
    os << '}';
    return os;
}
template <typename T> ostream& operator<<(ostream& os, const unordered_set<T>& s) {
    os << '{';
    for (auto itr = s.begin(); itr != s.end();) {
        os << *itr;
        if (++itr != s.end()) os << ',';
    }
    os << '}';
    return os;
}
template <typename T> ostream& operator<<(ostream& os, const deque<T>& v) {
    for (int i = 0; i < (int)v.size(); i++) {
        os << v[i] << (i + 1 == (int)v.size() ? "" : " ");
    }
    return os;
}

void debug_out() { cerr << '\n'; }
template <class Head, class... Tail> void debug_out(Head&& head, Tail&&... tail) {
    cerr << head;
    if (sizeof...(Tail) > 0) cerr << ", ";
    debug_out(move(tail)...);
}
#ifdef LOCAL
#define debug(...)                                                                   \
    cerr << " ";                                                                     \
    cerr << #__VA_ARGS__ << " :[" << __LINE__ << ":" << __FUNCTION__ << "]" << '\n'; \
    cerr << " ";                                                                     \
    debug_out(__VA_ARGS__)
#else
#define debug(...) 42
#endif

template <typename T> T gcd(T x, T y) { return y != 0 ? gcd(y, x % y) : x; }
template <typename T> T lcm(T x, T y) { return x / gcd(x, y) * y; }

template <class T1, class T2> inline bool chmin(T1& a, T2 b) {
    if (a > b) {
        a = b;
        return true;
    }
    return false;
}
template <class T1, class T2> inline bool chmax(T1& a, T2 b) {
    if (a < b) {
        a = b;
        return true;
    }
    return false;
}
#pragma endregion

/**
 * @brief modint
 * @docs docs/modulo/modint.md
 */
template <uint32_t mod> class modint {
    using i64 = int64_t;
    using u32 = uint32_t;
    using u64 = uint64_t;

public:
    u32 v;
    constexpr modint(const i64 x = 0) noexcept : v(x < 0 ? mod - 1 - (-(x + 1) % mod) : x % mod) {}
    constexpr u32& value() noexcept { return v; }
    constexpr const u32& value() const noexcept { return v; }
    constexpr modint operator+(const modint& rhs) const noexcept { return modint(*this) += rhs; }
    constexpr modint operator-(const modint& rhs) const noexcept { return modint(*this) -= rhs; }
    constexpr modint operator*(const modint& rhs) const noexcept { return modint(*this) *= rhs; }
    constexpr modint operator/(const modint& rhs) const noexcept { return modint(*this) /= rhs; }
    constexpr modint& operator+=(const modint& rhs) noexcept {
        v += rhs.v;
        if (v >= mod) v -= mod;
        return *this;
    }
    constexpr modint& operator-=(const modint& rhs) noexcept {
        if (v < rhs.v) v += mod;
        v -= rhs.v;
        return *this;
    }
    constexpr modint& operator*=(const modint& rhs) noexcept {
        v = (u64)v * rhs.v % mod;
        return *this;
    }
    constexpr modint& operator/=(const modint& rhs) noexcept { return *this *= rhs.pow(mod - 2); }
    constexpr modint pow(u64 exp) const noexcept {
        modint self(*this), res(1);
        while (exp > 0) {
            if (exp & 1) res *= self;
            self *= self;
            exp >>= 1;
        }
        return res;
    }
    constexpr modint& operator++() noexcept {
        if (++v == mod) v = 0;
        return *this;
    }
    constexpr modint& operator--() noexcept {
        if (v == 0) v = mod;
        return --v, *this;
    }
    constexpr modint operator++(int) noexcept {
        modint t = *this;
        return ++*this, t;
    }
    constexpr modint operator--(int) noexcept {
        modint t = *this;
        return --*this, t;
    }
    constexpr modint operator-() const noexcept { return modint(mod - v); }
    template <class T> friend constexpr modint operator+(T x, modint y) noexcept { return modint(x) + y; }
    template <class T> friend constexpr modint operator-(T x, modint y) noexcept { return modint(x) - y; }
    template <class T> friend constexpr modint operator*(T x, modint y) noexcept { return modint(x) * y; }
    template <class T> friend constexpr modint operator/(T x, modint y) noexcept { return modint(x) / y; }
    constexpr bool operator==(const modint& rhs) const noexcept { return v == rhs.v; }
    constexpr bool operator!=(const modint& rhs) const noexcept { return v != rhs.v; }
    constexpr bool operator!() const noexcept { return !v; }
    friend istream& operator>>(istream& s, modint& rhs) noexcept {
        i64 v;
        rhs = modint{(s >> v, v)};
        return s;
    }
    friend ostream& operator<<(ostream& s, const modint& rhs) noexcept { return s << rhs.v; }
};

/**
 * @brief UnionFind
 * @docs docs/datastructure/UnionFind.md
 */
struct UnionFind {
    int num;
    vector<int> par, rank;
    UnionFind(int n) : num(n), par(n), rank(n, 1) { iota(par.begin(), par.end(), 0); }
    int root(int x) { return (par[x] == x ? x : par[x] = root(par[x])); }
    bool merge(int x, int y) {
        x = root(x);
        y = root(y);
        if (x == y) return false;
        if (rank[x] < rank[y]) swap(x, y);
        par[y] = x;
        rank[x] += rank[y];
        num--;
        return true;
    }
    bool same(int x, int y) { return root(x) == root(y); }
    int size(int x) { return rank[root(x)]; }
    int count() { return num; }
    int operator[](int x) { return root(x); }
};

/**
 * @brief combination
 * @docs docs/combinatorics/combination.md
 */
template <class M> struct Combination {
    vector<M> _fac, _inv, _finv;
    Combination(int n) : _fac(n + 1), _inv(n + 1), _finv(n + 1) {
        _fac[0] = _finv[n] = _inv[0] = 1;
        for (int i = 1; i <= n; i++) _fac[i] = _fac[i - 1] * i;
        _finv[n] /= _fac[n];
        for (int i = n - 1; i >= 0; i--) _finv[i] = _finv[i + 1] * (i + 1);
        for (int i = 1; i <= n; i++) _inv[i] = _finv[i] * _fac[i - 1];
    }
    M fac(int k) const { return _fac[k]; }
    M finv(int k) const { return _finv[k]; }
    M inv(int k) const { return _inv[k]; }
    M P(int n, int r) const {
        if (n < 0 || r < 0 || n < r) return 0;
        return _fac[n] * _finv[n - r];
    }
    M C(int n, int r) const {
        if (n < 0 || r < 0 || n < r) return 0;
        return _fac[n] * _finv[r] * _finv[n - r];
    }
};

/**
 * @brief Number Theoretic Transform
 * @docs docs/convolution/NumberTheoreticTransform.md
 */
template <int mod> struct NumberTheoreticTransform {
    using Mint = modint<mod>;
    vector<Mint> roots;
    vector<int> rev;
    int base, max_base;
    Mint root;
    NumberTheoreticTransform() : base(1), rev{0, 1}, roots{Mint(0), Mint(1)} {
        int tmp = mod - 1;
        for (max_base = 0; tmp % 2 == 0; max_base++) tmp >>= 1;
        root = 2;
        while (root.pow((mod - 1) >> 1) == 1) root++;
        root = root.pow((mod - 1) >> max_base);
    }
    void ensure_base(int nbase) {
        if (nbase <= base) return;
        rev.resize(1 << nbase);
        for (int i = 0; i < (1 << nbase); i++) {
            rev[i] = (rev[i >> 1] >> 1) | ((i & 1) << (nbase - 1));
        }
        roots.resize(1 << nbase);
        for (; base < nbase; base++) {
            Mint z = root.pow(1 << (max_base - 1 - base));
            for (int i = 1 << (base - 1); i < (1 << base); i++) {
                roots[i << 1] = roots[i];
                roots[i << 1 | 1] = roots[i] * z;
            }
        }
    }
    void ntt(vector<Mint>& a) {
        const int n = a.size();
        int zeros = __builtin_ctz(n);
        ensure_base(zeros);
        int shift = base - zeros;
        for (int i = 0; i < n; i++) {
            if (i < (rev[i] >> shift)) {
                swap(a[i], a[rev[i] >> shift]);
            }
        }
        for (int k = 1; k < n; k <<= 1) {
            for (int i = 0; i < n; i += (k << 1)) {
                for (int j = 0; j < k; j++) {
                    Mint z = a[i + j + k] * roots[j + k];
                    a[i + j + k] = a[i + j] - z;
                    a[i + j] = a[i + j] + z;
                }
            }
        }
    }
    vector<Mint> multiply(vector<Mint> a, vector<Mint> b) {
        int need = a.size() + b.size() - 1;
        int nbase = 1;
        while ((1 << nbase) < need) nbase++;
        ensure_base(nbase);
        int sz = 1 << nbase;
        a.resize(sz, Mint(0));
        b.resize(sz, Mint(0));
        ntt(a);
        ntt(b);
        Mint inv_sz = 1 / Mint(sz);
        for (int i = 0; i < sz; i++) a[i] *= b[i] * inv_sz;
        reverse(a.begin() + 1, a.end());
        ntt(a);
        a.resize(need);
        return a;
    }
    vector<int> multiply(vector<int> a, vector<int> b) {
        vector<Mint> A(a.size()), B(b.size());
        for (int i = 0; i < a.size(); i++) A[i] = Mint(a[i]);
        for (int i = 0; i < b.size(); i++) B[i] = Mint(b[i]);
        vector<Mint> C = multiply(A, B);
        vector<int> res(C.size());
        for (int i = 0; i < C.size(); i++) res[i] = C[i].v;
        return res;
    }
};

const int INF = 1e9;
const long long IINF = 1e18;
const int dx[4] = {1, 0, -1, 0}, dy[4] = {0, 1, 0, -1};
const char dir[4] = {'D', 'R', 'U', 'L'};
// const long long MOD = 1000000007;
const long long MOD = 998244353;

using mint = modint<MOD>;

int main() {
    cin.tie(0);
    ios::sync_with_stdio(false);
    Combination<mint> COM(5010);
    int N, M;
    cin >> N >> M;
    vector<int> P(N);
    cin >> P;

    vector<vector<mint>> S(N + 1, vector<mint>(M + 1, 0));
    for (int i = 1; i <= N; i++) {
        for (int j = 1; j <= M; j++) {
            if (j > i) continue;
            if (j == 1)
                S[i][j] = 1;
            else
                S[i][j] = S[i - 1][j - 1] + S[i - 1][j] * j;
        }
    }

    UnionFind UF(N);
    for (int i = 0; i < N; i++) UF.merge(i, --P[i]);

    vector<int> v;
    vector<bool> check(N, false);
    for (int i = 0; i < N; i++) {
        if (check[UF[i]]) continue;
        check[UF[i]] = true;
        v.emplace_back(UF.size(i));
    }

    int n = v.size();
    vector<vector<mint>> a(n);
    for (int i = 0; i < n; i++) {
        for (int j = 0; j < v[i]; j++) {
            if (j == v[i] - 1)
                a[i].emplace_back(1);
            else
                a[i].emplace_back(COM.C(v[i], j));
        }
    }

    NumberTheoreticTransform<MOD> NTT;
    auto dfs = [&](auto self, int l, int r) -> vector<mint> {
        if (r - l == 1) return a[l];
        int mid = (l + r) >> 1;
        vector<mint> L = self(self, l, mid), R = self(self, mid, r);
        return NTT.multiply(L, R);
    };

    vector<mint> dp = dfs(dfs, 0, n);
    mint ans = 0;
    for (int i = 0; i < dp.size(); i++) {
        mint add = dp[i] * S[N - i][M];
        if (i & 1)
            ans -= add;
        else
            ans += add;
    }

    cout << ans << '\n';
}