def cmb(n, r, mod):
    if ( r<0 or r>n ):
        return 0
    r = min(r, n-r)
    return g1[n] * g2[r] * g2[n-r] % mod

mod = 998244353
N = 5000
g1 = [1]*(N+1)
g2 = [1]*(N+1)
inverse = [1]*(N+1)
for i in range( 2, N + 1 ):
    g1[i]=( ( g1[i-1] * i ) % mod )
    inverse[i]=( ( -inverse[mod % i] * (mod//i) ) % mod )
    g2[i]=( (g2[i-1] * inverse[i]) % mod )
inverse[0]=0

import numpy as np

N,M = map(int,input().split())
P = list(map(int,input().split()))

P = [P[i]-1 for i in range(N)]
cycle = []
used = [False]*N
for i in range(N):
    if not used[i]:
        used[i] = True
        c = 1
        pos = i
        while not used[P[pos]]:
            pos = P[pos]
            used[pos] = True
            c += 1
        cycle.append(c)

n = len(cycle)

binom_poly = np.array([1],np.int64)
for i in range(n):
    c = [cmb(cycle[i],j,mod)*pow(-1,j,mod) for j in range(1,cycle[i]+1)]
    c[0] = (c[0] + 1)
    c = np.array(c,np.int64) % mod
    binom_poly = np.convolve(binom_poly,c) % mod

Stirling = np.zeros((N+1,N+1),np.int64)
Stirling[:,1] = 1
for i in range(2,N+1):
    prod = np.array([j+2 for j in range(i-1)],np.int64)
    Stirling[i,2:i+1] = Stirling[i-1,1:i] + prod * Stirling[i-1,2:i+1]
    Stirling[i] %= mod


ans = 0
for i in range(N-n+1):
    ans += Stirling[n+i,M] * binom_poly[i]
    ans %= mod

ans *= (-1)**N
ans %= mod

print(ans)