from math import gcd

MOD = 1000000007

N, M = map(int, input().split())
A = [int(s) - 1 for s in input().split()]

used = [False] * N
cycles = [0] * (N+1)
for i in range(N):
    if used[i]: continue
    cnt = 0
    while not used[i]:
        used[i] = True
        i = A[i]
        cnt += 1
    cycles[cnt] += 1

fact = [0] * (N+1)
ifact = [0] * (N+1)
fact[0] = 1
ifact[0] = 1
for i in range(N):
    fact[i+1] = fact[i] * (i+1) % MOD
    ifact[i+1] = pow(fact[i+1], MOD - 2, MOD)

def binom(n, k):
    return fact[n] * ifact[k] % MOD * ifact[n-k] % MOD

ans = 1
for i in range(1, N+1):
    dp = [0] * (cycles[i] + 1)
    ms = [m for m in range(1, N+1) if m // gcd(m, M) == i]
    dp[0] = 1
    for j in range(1, cycles[i] + 1):
        for m in ms:
            if j - m//i >= 0:
                dp[j] += dp[j - m//i] * binom(j-1, m//i - 1) % MOD * fact[m//i - 1] % MOD * pow(i, m//i - 1, MOD) % MOD
                dp[j] %= MOD
    ans = ans * dp[cycles[i]] % MOD
print(ans)