# -*- coding: utf-8 -*-

"""

Created on Sat May 25 21:24:29 2019



@author: Yamazaki Kenichi

"""



N, M, K = list(map(int,input().split()))

mod = 10**9+7



def cmb(n, r, mod):

    if (r < 0 or r > n):

        return 0

    r = min(r, n-r)

    return g1[n] * g2[r] * g2[n-r] % mod



g1 = [1, 1] # 元テーブル

g2 = [1, 1] # 逆元テーブル

inv = [0, 1] # 逆元テーブル計算用テーブル



for i in range(2, N*M+1):

    g1.append((g1[-1] * i) % mod)

    inv.append((-inv[mod % i] * (mod//i)) % mod)

    g2.append((g2[-1] * inv[-1]) % mod)



def a(N,M):

    return N*(N+1)//2*(M+1) + M*(M+1)//2*(N+1)

def b(N):

    return N*(N+1)//2



ans = 0

for i in range(N):

    for j in range(M):

        ans += a(i,j) + a(N-i-1,j) + a(i,M-j-1) + a(N-i-1,M-j-1)

        ans -= b(i) + b(j) + b(N-i-1) + b(M-j-1)

        ans %= mod

#        print(i,j,a(i,j),a(N-i-1,j),a(i,M-j-1),a(N-i-1,M-j-1),b(i),b(j),ans)

ans *= g2[2]



ans *= cmb(N*M-2,K-2,mod)

ans %= mod



print(ans)

# -*- coding: utf-8 -*-

"""

Created on Wed May 29 22:49:19 2019



@author: Yamazaki Kenichi

"""



# -*- coding: utf-8 -*-

"""

Created on Sat May 25 21:24:29 2019



@author: Yamazaki Kenichi

"""



N, M, K = list(map(int,input().split()))

mod = 10**9+7



def cmb(n, r, mod):

    if (r < 0 or r > n):

        return 0

    r = min(r, n-r)

    return g1[n] * g2[r] * g2[n-r] % mod



g1 = [1, 1] # 元テーブル

g2 = [1, 1] # 逆元テーブル

inv = [0, 1] # 逆元テーブル計算用テーブル



for i in range(2, N*M+1):

    g1.append((g1[-1] * i) % mod)

    inv.append((-inv[mod % i] * (mod//i)) % mod)

    g2.append((g2[-1] * inv[-1]) % mod)



ans1 = 0

def c(N,M):

    res = 0

    for i in range(1,N):

        res += i*(N-i)*M*M

    return res

ans1 += c(N,M) + c(M,N)

ans1 %= mod



ans1 *= cmb(N*M-2,K-2,mod)

ans1 %= mod



print(ans1)

# -*- coding: utf-8 -*-
"""
Created on Sat May 25 21:24:29 2019
@author: Yamazaki Kenichi
"""
N, M, K = list(map(int, input().split()))
mod = 10**9 + 7


def cmb(n, r, mod):
    if r < 0 or r > n:
        return 0
    r = min(r, n - r)
    return g1[n] * g2[r] * g2[n - r] % mod


g1 = [1, 1]  # 元テーブル
g2 = [1, 1]  # 逆元テーブル
inv = [0, 1]  # 逆元テーブル計算用テーブル
for i in range(2, N * M + 1):
    g1.append((g1[-1] * i) % mod)
    inv.append((-inv[mod % i] * (mod // i)) % mod)
    g2.append((g2[-1] * inv[-1]) % mod)


def a(N, M):
    return N * (N + 1) // 2 * (M + 1) + M * (M + 1) // 2 * (N + 1)


def b(N):
    return N * (N + 1) // 2


ans = 0
for i in range(N):
    for j in range(M):
        ans += a(i, j) + a(N - i - 1, j) + a(i, M - j - 1) + a(N - i - 1, M - j - 1)
        ans -= b(i) + b(j) + b(N - i - 1) + b(M - j - 1)
        ans %= mod
#        print(i,j,a(i,j),a(N-i-1,j),a(i,M-j-1),a(N-i-1,M-j-1),b(i),b(j),ans)
ans *= g2[2]
ans *= cmb(N * M - 2, K - 2, mod)
ans %= mod
print(ans)

# -*- coding: utf-8 -*-
"""
Created on Wed May 29 22:49:19 2019
@author: Yamazaki Kenichi
"""
# -*- coding: utf-8 -*-
"""
Created on Sat May 25 21:24:29 2019
@author: Yamazaki Kenichi
"""
N, M, K = list(map(int, input().split()))
mod = 10**9 + 7


def cmb(n, r, mod):
    if r < 0 or r > n:
        return 0
    r = min(r, n - r)
    return g1[n] * g2[r] * g2[n - r] % mod


g1 = [1, 1]  # 元テーブル
g2 = [1, 1]  # 逆元テーブル
inv = [0, 1]  # 逆元テーブル計算用テーブル
for i in range(2, N * M + 1):
    g1.append((g1[-1] * i) % mod)
    inv.append((-inv[mod % i] * (mod // i)) % mod)
    g2.append((g2[-1] * inv[-1]) % mod)
ans1 = 0


def c(N, M):
    res = 0
    for i in range(1, N):
        res += i * (N - i) * M * M
    return res


ans1 += c(N, M) + c(M, N)
ans1 %= mod
ans1 *= cmb(N * M - 2, K - 2, mod)
ans1 %= mod
print(ans1)

+# -*- coding: utf-8 -*- +""" +Created on Wed May 29 22:49:19 2019 +@author: Yamazaki Kenichi +""" +ans1 = 0 -def a(N, M): -    return N * (N + 1) // 2 * (M + 1) + M * (M + 1) // 2 * (N + 1) +def c(N, M): +    res = 0 +    for i in range(1, N): +        res += i * (N - i) * M * M +    return res -def b(N): -    return N * (N + 1) // 2 - - -ans = 0 -for i in range(N): -    for j in range(M): -        ans += a(i, j) + a(N - i - 1, j) + a(i, M - j - 1) + a(N - i - 1, M - j - 1) -        ans -= b(i) + b(j) + b(N - i - 1) + b(M - j - 1) -        ans %= mod -#        print(i,j,a(i,j),a(N-i-1,j),a(i,M-j-1),a(N-i-1,M-j-1),b(i),b(j),ans) -ans *= g2[2] -ans *= cmb(N * M - 2, K - 2, mod) -ans %= mod -print(ans) +ans1 += c(N, M) + c(M, N) +ans1 %= mod +ans1 *= cmb(N * M - 2, K - 2, mod) +ans1 %= mod +print(ans1)