Problem: Consider the following experiment. You have a deck of m cards, and exactly one card is a joker. n times, you do the following: shuffle the deck, take the top card of the deck, look at it and return it into the deck.

Let x be the number of times you have taken the joker out of the deck during this experiment. Assuming that every time you shuffle the deck, all m! possible permutations of cards are equiprobable, what is the expected value of x^k? Print the answer modulo 998244353.

Input

The only line contains three integers n, m and k (1 ≤ n, m < 998244353, 1 ≤ k ≤ 5000).

Output

Print one integer — the expected value of x^k, taken modulo 998244353 (the answer can always be represented as an irreducible fraction a/b, where b mod 998244353 ≠ 0; you have to print a ⋅ b^{-1} mod 998244353).

Examples

Input


1 1 1


Output


1


Input


1 1 5000


Output


1


Input


2 2 2


Output


499122178


Input


998244352 1337 5000


Output


326459680

Solution (in PYTHON3):

Solution:
def inv(a):
	return pow(a, MOD-2, MOD) %MOD

def fat(a):
	ans = 1
	for i in range(1, a+1):
		ans = (ans*i)%MOD
	return ans

MOD = 998244353
n, m, k = map(int, input().split())
p = inv(m)

# O(Burro) O(n2)-> Fórmula da experança = sum(x^k * C(n, x) * p^x * q^(n-x))
'''
resp = 0
q = (1 - p + MOD) % MOD
for x in range(1, n+1):
	resp += pow(x, k, MOD) %MOD * fat(n) %MOD * invfat(n-x) %MOD * invfat(x) %MOD *pow(p, x, MOD) %MOD * pow(q, n-x, MOD) %MOD
'''
# O(menos burro) O(nlog(k)) -> atualiza somatório usando valores ja calculados
if n<=k:
	q = (1 - p + MOD) % MOD
	inv_q = inv(q)
	p_aux = p
	q_aux = pow(q, n-1, MOD)
	fn = n
	resp = n * p%MOD * q_aux%MOD
	resp = resp%MOD

	for i in range(2, n+1):
		x = pow(i, k, MOD)
		p_aux = p_aux * p %MOD
		q_aux = q_aux * inv_q	
		fn = fn*(n-i+1)%MOD*inv(i)%MOD
		
		resp = resp + x * fn %MOD * p_aux %MOD * q_aux %MOD
		resp = resp%MOD
	print(resp)

# O(inteligente) O(k2) -> A partir da FGM M(X), identifica padrão das derivadas
# k-ésima derivada de M(X) = E(x^k)
# E(x^k) = n!/(n-k)! * p^k + k*(deriv[k-1] - sum(ind[i]*deriv[i])) + sum(ind[i]*deriv[i+1])
else:
	deriv = [(n*p)%MOD] #E(x) = np
	resp = n*n%MOD*p%MOD*p%MOD - n*p%MOD*p%MOD + n*p%MOD #E(x^2) = n^2p^2 - np^2 + np
	deriv.append(resp%MOD)
	fn = (n*(n-1))%MOD
	v=[1];
	
	for i in range(3, k+1):
		fn = (fn * (n-i+1) %MOD)%MOD
		w = [(-(i-1)*v[0])%MOD]	
		for j in range(len(v)-1):
			w.append((v[j] - (i-1)*v[j+1]%MOD)%MOD) 
		w.append((v[-1] + i-1)%MOD)
		v = tuple(w)

		resp = (fn * pow(p, i, MOD))%MOD
		for j in range(len(v)):
			resp = (resp + v[j]*deriv[j]%MOD)%MOD	
			resp = resp%MOD
		resp %= MOD
		deriv.append(resp)

	print(deriv[k-1])