import sys from collections import defaultdict, Counter, deque from itertools import permutations, combinations, product, combinations_with_replacement, groupby, accumulate import operator from math import sqrt, gcd, factorial # from math import isqrt, prod,comb # python3.8用(notpypy) #from bisect import bisect_left,bisect_right #from functools import lru_cache,reduce #from heapq import heappush,heappop,heapify,heappushpop,heapreplace #import numpy as np #import networkx as nx #from networkx.utils import UnionFind #from numba import njit, b1, i1, i4, i8, f8 #from scipy.sparse import csr_matrix #from scipy.sparse.csgraph import shortest_path, floyd_warshall, dijkstra, bellman_ford, johnson, NegativeCycleError # numba例 @njit(i1(i4[:], i8[:, :]),cache=True) 引数i4配列、i8 2次元配列,戻り値i1 def input(): return sys.stdin.readline().rstrip() def divceil(n, k): return 1+(n-1)//k # n/kの切り上げを返す def yn(hantei, yes='Yes', no='No'): print(yes if hantei else no) class PrepereFactorial2: # maxnumまでの階乗を事前計算して、順列、組み合わせ、重複組み合わせを計算するクラス。逆元のテーブルもpow無しで前計算する。maxnumに比べて関数呼び出しが多いならこちら def __init__(self, maxnum=3*10**5, mod=10**9+7): self.factorial = [1]*(maxnum+1) modinv_table = [-1] * (maxnum+1) modinv_table[1] = 1 for i in range(2, maxnum+1): self.factorial[i] = (self.factorial[i-1]*i) % mod modinv_table[i] = (-modinv_table[mod % i] * (mod // i)) % mod self.invfactorial = [1]*(maxnum+1) for i in range(1, maxnum+1): self.invfactorial[i] = self.invfactorial[i-1]*modinv_table[i] % mod self.mod = mod def permutation(self, n, r): return self.factorial[n]*self.invfactorial[n-r] % self.mod def combination(self, n, r): return self.permutation(n, r)*self.invfactorial[r] % self.mod def combination_with_repetition(self, n, r): return self.combination(n+r-1, r) def main(): mod = 10**9+7 mod2 = 998244353 n, m, k = map(int, input().split()) pf = PrepereFactorial2(max(n, m)+5, mod2) p1 = pf.combination(n, k-2)*pf.combination(m, k-2) for i in range(1, k-1): p1 *= i p1 %= mod2 amarin = n-k+2 amarim = m-k+2 p2 = 0 inv2 = pow(2, mod2-2, mod2) inv3 = pow(3, mod2-2, mod2) inv4 = pow(4, mod2-2, mod2) # 解説2.1 tmp = ((k-2)**2-k+2) p2 += tmp*(tmp-2)*inv2+tmp*inv4 # 解説2.2 tmp2 = amarin*(k-2) p2 += tmp2*(k-3)*inv3 # 2.2.1 p2 += tmp2*(tmp-k+3)*inv2 # 2.2.1 p2 += tmp2*(k-4+amarin)*inv3*inv2 # 2.2.2 p2 += tmp2*(tmp2-(k-3+amarin))*inv4*inv2 # 2.2.2 p2 += tmp2*amarim*(k-3)*inv4 # 2.2.3 # 解説2.3 tmp3 = amarim*(k-2) p2 += tmp3*(k-3)*inv3 p2 += tmp3*(tmp-k+3)*inv2 p2 += tmp3*(k-4+amarin)*inv3*inv2 p2 += tmp3*(tmp3-(k-3+amarin))*inv4*inv2 print((p1*p2) % mod2) if __name__ == '__main__': main()