import sys
input = lambda : sys.stdin.readline().rstrip()

sys.setrecursionlimit(2*10**5+10)
write = lambda x: sys.stdout.write(x+"\n")

n,m = list(map(int, input().split()))
p = list(map(lambda x: int(x)-1, input().split()))
M = 998244353
N = n+m+100 # 必要なテーブルサイズ
g1 = [0] * (N+1) # 元テーブル
g2 = [0] * (N+1) #逆元テーブル
inverse = [0] * (N+1) #逆元テーブル計算用テーブル
g1[0] = g1[1] = g2[0] = g2[1] = 1
inverse[0], inverse[1] = [0, 1] 
for i in range( 2, N + 1 ):
    g1[i] = ( g1[i-1] * i ) % M 
    inverse[i] = ( -inverse[M % i] * (M//i) ) % M # ai+b==0 mod M <=> i==-b*a^(-1) <=> i^(-1)==-b^(-1)*aより
    g2[i] = (g2[i-1] * inverse[i]) % M 
def cmb(n, r, M):
    if ( r<0 or r>n ):
        return 0
    r = min(r, n-r)
    return ((g1[n] * g2[r] % M) * g2[n-r]) % M
def perm(n, r, M):
    if (r<0 or r>n):
        return 0
    return (g1[n] * g2[n-r]) % M

def part(p):
    n = len(p)
    done = [0]*n
    ans = []
    for i in range(n):
        if done[i]:
            continue
        l = [i]
        i0 = i
        done[i] = 1
        while p[i]!=i0:
            i = p[i]
            l.append(i)
            done[i] = 1
        ans.append(l)
    return ans
d = {}
def sub(i,j):
    if (i,j) in d:
        return d[i,j]
    dp0 = dp1 = 0
    dp0 = j
    for ii in range(i-1):
        dp0, dp1 = dp1, dp1*(j-2) + dp0*(j-1)
        dp0 %= M
        dp1 %= M
    ans = dp1
    if i==1:
        ans = j
    d[i,j] = ans
    return ans
l = part(p)
nums = [len(item) for item in l]
ans = 0
for i in range(m):
    s = 1 if i%2==0 else -1
    val = s
    for num in nums:
        val *= sub(num, m-i)
        val %= M
    ans += val * cmb(m, i, M)
#     ans += val * pow(m-i, len(l), M)
#     print(i,val%M,s)
ans *= g2[m]
print(ans%M)