## https://yukicoder.me/problems/no/1392

MOD = 998244353

# ソースコードの出典URL: https://github.com/LyricalMaestro/at_coder_snippets/blob/af67863a2fe7f16cce8325bbc531f89968bfa525/src/conbination.py

class CombinationCalculator:
    """
    modを考慮したPermutation, Combinationを計算するためのクラス
    """    
    def __init__(self, size, mod):
        self.mod = mod
        self.factorial = [0] * (size + 1)
        self.factorial[0] = 1
        for i in range(1, size + 1):
            self.factorial[i] = (i * self.factorial[i - 1]) % self.mod
        
        self.inv_factorial = [0] * (size + 1)
        self.inv_factorial[size] = pow(self.factorial[size], self.mod - 2, self.mod)

        for i in reversed(range(size)):
            self.inv_factorial[i] = ((i + 1) * self.inv_factorial[i + 1]) % self.mod

    def calc_combination(self, n, r):
        if n < 0 or n < r or r < 0:
            return 0

        if r == 0 or n == r:
            return 1
        
        ans = self.inv_factorial[n - r] * self.inv_factorial[r]
        ans %= self.mod
        ans *= self.factorial[n]
        ans %= self.mod
        return ans
    
    def calc_permutation(self, n, r):
        if n < 0 or n < r:
            return 0

        ans = self.inv_factorial[n - r]
        ans *= self.factorial[n]
        ans %= self.mod
        return ans
        

def main():
    N, M = map(int, input().split())
    P = list(map(int, input().split()))
    if M == 1:
        print(0)
        return


    cycles_id = 0
    passed = [-1] * N
    for s_i in range(N):
        if passed[s_i] == -1:
            passed[s_i] = cycles_id

            p = P[s_i] - 1
            while p != s_i:
                passed[p] = cycles_id
                p = P[p] - 1
            cycles_id += 1

    cycles = [0] * cycles_id
    for i in range(N):
        cycles[passed[i]] += 1

    combi = CombinationCalculator(N + M, MOD)
    answer = 0
    for m in reversed(range(2, M + 1)):

        ans = 1
        for c in cycles:
            dp = [1, 0]
            for _ in range(1, c):
                new_dp = [0, 0]
                new_dp[1] += (dp[0] * (m - 1)) % MOD
                new_dp[1] %= MOD
                new_dp[0] += dp[1]
                new_dp[0] %= MOD
                new_dp[1] += (dp[1] * (m - 2)) % MOD
                new_dp[1] %= MOD
                dp = new_dp
            a = dp[1]
            a *= m
            a %= MOD
            ans *= a
            ans %= MOD
        ans2 = (ans * combi.calc_combination(M, m)) % MOD
        ans2 *= pow(-1, M - m, MOD)
        ans2 %= MOD
        answer += ans2
        answer %= MOD

    answer *= combi.inv_factorial[M]
    answer %= MOD
    print(answer)
        

            

                




if __name__ == "__main__":
    main()