MOD = 998244353
MAX = 5000
fac = [1] * (MAX + 1)
for i in range(MAX):
    fac[i + 1] = fac[i] * (i + 1) % MOD
inv = [1] * (MAX + 1)
inv[MAX] = pow(fac[MAX], MOD - 2, MOD)
for i in range(MAX, 0, -1):
    inv[i - 1] = inv[i] * i % MOD

n, m = map(int, input().split(' '))
p = [*map(int, input().split(' '))]
assert 2 <= n <= 5000
assert 1 <= m <= n
assert len(p) == n
for i in range(n):
    assert 1 <= p[i] <= n
    p[i] -= 1
    assert p[i] != i

# 順列をサイクルに分解
cycle = []
used = [False] * n
for i in range(n):
    if used[i]:
        continue
    l = 0
    while not used[i]:
        used[i] = True
        l += 1
        i = p[i]
    cycle.append(l)

# 包除原理 a[i] := 1 ~ N を i 個の区別するグループに分ける分け方 整数が入っていないグループがあってもOK
a = [1] * (m + 1)
for i in range(2, m + 1):
    for l in cycle:
        a[i] *= pow(i-1, l, MOD) + (1 - i if l & 1 else i - 1)
        a[i] %= MOD

ans = 0
for i in range(2, m + 1):
    ans += a[i] * fac[m] * inv[i] * inv[m - i] * (-1 if (m ^ i) & 1 else 1)
ans *= inv[m]
print(ans % MOD)