Buggy python submission (verdict: Time Limit Exceeded):
from math import factorial
N, M, K = map(int, input().split())

MOD = 10**9+7

def comb(n, r):
    r = n-r if n-r < r else r
    if r == 0:
        return 1
    ndfact = 1
    for i in range(n, n-r, -1):
        ndfact *= i
    return ndfact // factorial(r)

p = comb(N*M-2, K-2) % MOD
ans = 0
for i in range(N):
    for j in range(M):
        if i == 0 and j == 0:
            continue
        d = i+j
        cnt = (N-i) * (M-j)
        if i != 0 and j != 0:
            cnt *= 2
        ans += d * cnt
        ans %= MOD

print((ans*p)%MOD)


Fixed submission:
from math import factorial
N, M, K = map(int, input().split())

MOD = 10**9+7

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

def comb(n, r):
    r = n-r if n-r < r else r
    return fact[n] * pow(fact[r], MOD-2, MOD) * pow(fact[n-r], MOD-2, MOD) % MOD

p = comb(N*M-2, K-2)
ans = 0
for i in range(N):
    for j in range(M):
        if i == 0 and j == 0:
            continue
        d = i+j
        cnt = (N-i) * (M-j)
        if i != 0 and j != 0:
            cnt *= 2
        ans += d * cnt % MOD
ans = ans * p % MOD

print(ans)

Buggy python submission (verdict: Runtime Error):
from math import factorial
N, M, K = map(int, input().split())

MOD = 10**9+7

def comb(n, r):
    r = n-r if n-r < r else r
    if r == 0:
        return 1
    ndfact = 1
    for i in range(n, n-r, -1):
        ndfact *= i
    return ndfact // factorial(r)

p = comb(N*M-2, K-2) % MOD
ans = 0
for i in range(N):
    for j in range(M):
        if i == 0 and j == 0:
            continue
        d = i+j
        cnt = (N-i) * (M-j)
        if i != 0 and j != 0:
            cnt *= 2
        ans += d * cnt
        asn %= MOD

print((ans*p)%MOD)


Fixed submission:
from math import factorial
N, M, K = map(int, input().split())

MOD = 10**9+7

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

def comb(n, r):
    r = n-r if n-r < r else r
    return fact[n] * pow(fact[r], MOD-2, MOD) * pow(fact[n-r], MOD-2, MOD) % MOD

p = comb(N*M-2, K-2)
ans = 0
for i in range(N):
    for j in range(M):
        if i == 0 and j == 0:
            continue
        d = i+j
        cnt = (N-i) * (M-j)
        if i != 0 and j != 0:
            cnt *= 2
        ans += d * cnt % MOD
ans = ans * p % MOD

print(ans)

Buggy python submission (verdict: Time Limit Exceeded):
from math import factorial
N, M, K = map(int, input().split())

MOD = 10**9+7

def comb(n, r):
    r = n-r if n-r < r else r
    if r == 0:
        return 1
    ndfact = 1
    for i in range(n, n-r, -1):
        ndfact *= i
    return ndfact // factorial(r)

p = comb(N*M-2, K-2)
ans = 0
for i in range(N):
    for j in range(M):
        if i == 0 and j == 0:
            continue
        d = i+j
        #print(i, j, calc_rec_num(N, M, 0, 0, i, j))
        cnt = (N-i) * (M-j)
        if i != 0 and j != 0:
            cnt *= 2
        ans += d * cnt
        #if ans > DIV:
        #    ans %= DIV
        #print(ans)

print((ans*p)%MOD)


Fixed submission:
from math import factorial
N, M, K = map(int, input().split())

MOD = 10**9+7

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

def comb(n, r):
    r = n-r if n-r < r else r
    return fact[n] * pow(fact[r], MOD-2, MOD) * pow(fact[n-r], MOD-2, MOD) % MOD

p = comb(N*M-2, K-2)
ans = 0
for i in range(N):
    for j in range(M):
        if i == 0 and j == 0:
            continue
        d = i+j
        cnt = (N-i) * (M-j)
        if i != 0 and j != 0:
            cnt *= 2
        ans += d * cnt % MOD
ans = ans * p % MOD

print(ans)

Buggy python submission (verdict: Time Limit Exceeded):
from math import factorial
N, M, K = map(int, input().split())

MOD = 10**9+7

def comb(n, r):
    r = n-r if n-r < r else r
    if r == 0:
        return 1
    ndfact = 1
    for i in range(n, n-r, -1):
        ndfact *= i
    return ndfact // factorial(r)

p = comb(N*M-2, K-2)
ans = 0
for i in range(N):
    for j in range(M):
        if i == 0 and j == 0:
            continue
        d = i+j
        #print(i, j, calc_rec_num(N, M, 0, 0, i, j))
        cnt = (N-i) * (M-j)
        if i != 0 and j != 0:
            cnt *= 2
        ans += d * cnt
        #if ans > DIV:
        #    ans %= DIV
        #print(ans)

print((ans*p)%MOD)


Fixed submission:
from math import factorial
N, M, K = map(int, input().split())

MOD = 10**9+7

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

def comb(n, r):
    r = n-r if n-r < r else r
    return fact[n] * pow(fact[r], MOD-2, MOD) * pow(fact[n-r], MOD-2, MOD) % MOD

p = comb(N*M-2, K-2)
ans = 0
for i in range(N):
    for j in range(M):
        if i == 0 and j == 0:
            continue
        d = i+j
        cnt = (N-i) * (M-j)
        if i != 0 and j != 0:
            cnt *= 2
        ans += d * cnt % MOD
ans = ans * p % MOD

print(ans)

Buggy python submission (verdict: Time Limit Exceeded):
N, M, K = map(int, input().split())

MOD = 10**9+7
fact = [1 for i in range(N*M+1)]
for i in range(2, N*M+1):
    fact[i] = fact[i-1] * i

def comb(n, r):
    if n == 0 or r == 0:
        return 1
    return fact[n] // fact[n-r] // fact[r]

p = comb(N*M-2, K-2)
ans = 0
for i in range(N):
    for j in range(M):
        if i == 0 and j == 0:
            continue
        d = i+j
        #print(i, j, calc_rec_num(N, M, 0, 0, i, j))
        cnt = (N-i) * (M-j)
        if i != 0 and j != 0:
            cnt *= 2
        ans += d * cnt
        #if ans > DIV:
        #    ans %= DIV
        #print(ans)

print((ans*p)%MOD)


Fixed submission:
from math import factorial
N, M, K = map(int, input().split())

MOD = 10**9+7

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

def comb(n, r):
    r = n-r if n-r < r else r
    return fact[n] * pow(fact[r], MOD-2, MOD) * pow(fact[n-r], MOD-2, MOD) % MOD

p = comb(N*M-2, K-2)
ans = 0
for i in range(N):
    for j in range(M):
        if i == 0 and j == 0:
            continue
        d = i+j
        cnt = (N-i) * (M-j)
        if i != 0 and j != 0:
            cnt *= 2
        ans += d * cnt % MOD
ans = ans * p % MOD

print(ans)

Buggy python submission (verdict: Time Limit Exceeded):
N, M, K = map(int, input().split())

MOD = 10**9+7
fact = [1 for i in range(N*M+1)]
for i in range(2, N*M+1):
    fact[i] = fact[i-1] * i

def comb(n, r):
    return fact[n] // fact[n-r] // fact[r]

p = comb(N*M-2, K-2)
ans = 0
for i in range(N):
    for j in range(M):
        if i == 0 and j == 0:
            continue
        d = i+j
        #print(i, j, calc_rec_num(N, M, 0, 0, i, j))
        cnt = (N-i) * (M-j)
        if i != 0 and j != 0:
            cnt *= 2
        ans += d * cnt
        #if ans > DIV:
        #    ans %= DIV
        #print(ans)

print((ans*p)%MOD)


Fixed submission:
from math import factorial
N, M, K = map(int, input().split())

MOD = 10**9+7

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

def comb(n, r):
    r = n-r if n-r < r else r
    return fact[n] * pow(fact[r], MOD-2, MOD) * pow(fact[n-r], MOD-2, MOD) % MOD

p = comb(N*M-2, K-2)
ans = 0
for i in range(N):
    for j in range(M):
        if i == 0 and j == 0:
            continue
        d = i+j
        cnt = (N-i) * (M-j)
        if i != 0 and j != 0:
            cnt *= 2
        ans += d * cnt % MOD
ans = ans * p % MOD

print(ans)

Buggy python submission (verdict: Runtime Error):
N, M, K = map(int, input().split())

MOD = 10**9+7
fact = [1 for i in range(N+M+1)]
for i in range(2, N*M+1):
    fact[i] = fact[i-1] * i

def comb(n, r):
    return fact[n] // fact[n-r] // fact[r]

p = comb(N*M-2, K-2)
ans = 0
for i in range(N):
    for j in range(M):
        if i == 0 and j == 0:
            continue
        d = i+j
        #print(i, j, calc_rec_num(N, M, 0, 0, i, j))
        cnt = (N-i) * (M-j)
        if i != 0 and j != 0:
            cnt *= 2
        ans += d * cnt
        #if ans > DIV:
        #    ans %= DIV
        #print(ans)

print((ans*p)%MOD)


Fixed submission:
from math import factorial
N, M, K = map(int, input().split())

MOD = 10**9+7

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

def comb(n, r):
    r = n-r if n-r < r else r
    return fact[n] * pow(fact[r], MOD-2, MOD) * pow(fact[n-r], MOD-2, MOD) % MOD

p = comb(N*M-2, K-2)
ans = 0
for i in range(N):
    for j in range(M):
        if i == 0 and j == 0:
            continue
        d = i+j
        cnt = (N-i) * (M-j)
        if i != 0 and j != 0:
            cnt *= 2
        ans += d * cnt % MOD
ans = ans * p % MOD

print(ans)

Buggy python submission (verdict: Runtime Error):
N, M, K = map(int, input().split())

MOD = 10**9+7
fact = [1 for i in range(N+1)]
for i in range(2, N+1):
    fact[i] = fact[i-1] * i

def comb(n, r):
    return fact[n] // fact[n-r] // fact[r]

p = comb(N*M-2, K-2)
ans = 0
for i in range(N):
    for j in range(M):
        if i == 0 and j == 0:
            continue
        d = i+j
        #print(i, j, calc_rec_num(N, M, 0, 0, i, j))
        cnt = (N-i) * (M-j)
        if i != 0 and j != 0:
            cnt *= 2
        ans += d * cnt
        #if ans > DIV:
        #    ans %= DIV
        #print(ans)

print((ans*p)%MOD)


Fixed submission:
from math import factorial
N, M, K = map(int, input().split())

MOD = 10**9+7

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

def comb(n, r):
    r = n-r if n-r < r else r
    return fact[n] * pow(fact[r], MOD-2, MOD) * pow(fact[n-r], MOD-2, MOD) % MOD

p = comb(N*M-2, K-2)
ans = 0
for i in range(N):
    for j in range(M):
        if i == 0 and j == 0:
            continue
        d = i+j
        cnt = (N-i) * (M-j)
        if i != 0 and j != 0:
            cnt *= 2
        ans += d * cnt % MOD
ans = ans * p % MOD

print(ans)

Buggy python submission (verdict: Runtime Error):
N, M, K = map(int, input().split())

MOD = 10**9+7
fact = [1 for i in range(N+1)]
for i in range(2, N+1):
    fact[i] = fact[i-1] * i

def comb(n, r):
    return fact[n] // fact[n-r] // fact[r]

p = comb(K-2, N*M-2)
ans = 0
for i in range(N):
    for j in range(M):
        if i == 0 and j == 0:
            continue
        d = i+j
        #print(i, j, calc_rec_num(N, M, 0, 0, i, j))
        cnt = (N-i) * (M-j)
        if i != 0 and j != 0:
            cnt *= 2
        ans += d * cnt
        #if ans > DIV:
        #    ans %= DIV
        #print(ans)

print((ans*p)%MOD)


Fixed submission:
from math import factorial
N, M, K = map(int, input().split())

MOD = 10**9+7

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

def comb(n, r):
    r = n-r if n-r < r else r
    return fact[n] * pow(fact[r], MOD-2, MOD) * pow(fact[n-r], MOD-2, MOD) % MOD

p = comb(N*M-2, K-2)
ans = 0
for i in range(N):
    for j in range(M):
        if i == 0 and j == 0:
            continue
        d = i+j
        cnt = (N-i) * (M-j)
        if i != 0 and j != 0:
            cnt *= 2
        ans += d * cnt % MOD
ans = ans * p % MOD

print(ans)

Buggy python submission (verdict: Time Limit Exceeded):
from math import factorial

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

DIV = 10**9+7

#def comb(l, r):
#    if l == 0:
#        return 1
#    val = 1
#    for i in range(r, r-l, -1):
#        val *= i
#    for i in range(l, 0, -1):
#        val //= i
#    return val

#p = comb(K-2, N*M-2)
p = factorial(N*M-2) // factorial(K-2) // factorial((N*M-2) - (K-2))
#print(K-2, N*M-2, p)
ans = 0
for i in range(N):
    for j in range(M):
        if i == 0 and j == 0:
            continue
        d = i+j
        #print(i, j, calc_rec_num(N, M, 0, 0, i, j))
        cnt = (N-i) * (M-j)
        if i != 0 and j != 0:
            cnt *= 2
        ans += d * cnt
        #if ans > DIV:
        #    ans %= DIV
        #print(ans)

print((ans*p)%DIV)


Fixed submission:
from math import factorial
N, M, K = map(int, input().split())

MOD = 10**9+7

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

def comb(n, r):
    r = n-r if n-r < r else r
    return fact[n] * pow(fact[r], MOD-2, MOD) * pow(fact[n-r], MOD-2, MOD) % MOD

p = comb(N*M-2, K-2)
ans = 0
for i in range(N):
    for j in range(M):
        if i == 0 and j == 0:
            continue
        d = i+j
        cnt = (N-i) * (M-j)
        if i != 0 and j != 0:
            cnt *= 2
        ans += d * cnt % MOD
ans = ans * p % MOD

print(ans)

Buggy python submission (verdict: Runtime Error):
N, M, K = map(int, input().split())

DIV = 10**9+7

def comb(l, r):
    if l == 0:
        return 1
    val = 1
    for i in range(r, r-l, -1):
        val *= i
    for i in range(l, 0, -1):
        val //= i
    return val


#p = comb(K-2, N*M-2)
#print(K-2, N*M-2, p)
ans = 0
for i in range(N):
    for j in range(M):
        if i == 0 and j == 0:
            continue
        d = i+j
        #print(i, j, calc_rec_num(N, M, 0, 0, i, j))
        cnt = (N-i) * (M-j)
        if i != 0 and j != 0:
            cnt *= 2
        ans += d * cnt
        #if ans > DIV:
        #    ans %= DIV
        #print(ans)

print((ans*p)%DIV)


Fixed submission:
from math import factorial
N, M, K = map(int, input().split())

MOD = 10**9+7

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

def comb(n, r):
    r = n-r if n-r < r else r
    return fact[n] * pow(fact[r], MOD-2, MOD) * pow(fact[n-r], MOD-2, MOD) % MOD

p = comb(N*M-2, K-2)
ans = 0
for i in range(N):
    for j in range(M):
        if i == 0 and j == 0:
            continue
        d = i+j
        cnt = (N-i) * (M-j)
        if i != 0 and j != 0:
            cnt *= 2
        ans += d * cnt % MOD
ans = ans * p % MOD

print(ans)

Buggy python submission (verdict: Time Limit Exceeded):
N, M, K = map(int, input().split())

DIV = 10**9+7

def comb(l, r):
    if l == 0:
        return 1
    val = 1
    for i in range(r, r-l, -1):
        val *= i
    for i in range(l, 0, -1):
        val //= i
    return val


p = comb(K-2, N*M-2)
#print(K-2, N*M-2, p)
ans = 0
for i in range(N):
    for j in range(M):
        if i == 0 and j == 0:
            continue
        d = i+j
        #print(i, j, calc_rec_num(N, M, 0, 0, i, j))
        cnt = (N-i) * (M-j)
        if i != 0 and j != 0:
            cnt *= 2
        ans += d * cnt
        #if ans > DIV:
        #    ans %= DIV
        #print(ans)

print((ans*p)%DIV)


Fixed submission:
from math import factorial
N, M, K = map(int, input().split())

MOD = 10**9+7

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

def comb(n, r):
    r = n-r if n-r < r else r
    return fact[n] * pow(fact[r], MOD-2, MOD) * pow(fact[n-r], MOD-2, MOD) % MOD

p = comb(N*M-2, K-2)
ans = 0
for i in range(N):
    for j in range(M):
        if i == 0 and j == 0:
            continue
        d = i+j
        cnt = (N-i) * (M-j)
        if i != 0 and j != 0:
            cnt *= 2
        ans += d * cnt % MOD
ans = ans * p % MOD

print(ans)

Buggy python submission (verdict: Time Limit Exceeded):
N, M, K = map(int, input().split())

DIV = 10**9+7

def comb(l, r):
    if l == 0:
        return 1
    val = 1
    for i in range(r, r-l, -1):
        val *= i
    for i in range(l, 0, -1):
        val //= i
    return val


p = comb(K-2, N*M-2)
#print(K-2, N*M-2, p)
ans = 0
for i in range(N):
    for j in range(M):
        if i == 0 and j == 0:
            continue
        d = i+j
        #print(i, j, calc_rec_num(N, M, 0, 0, i, j))
        cnt = (N-i) * (M-j)
        if i != 0 and j != 0:
            cnt *= 2
        ans += d * cnt
        #if ans > DIV:
        #    ans %= DIV
        #print(ans)

print((ans*p)%DIV)


Fixed submission:
from math import factorial
N, M, K = map(int, input().split())

MOD = 10**9+7

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

def comb(n, r):
    r = n-r if n-r < r else r
    return fact[n] * pow(fact[r], MOD-2, MOD) * pow(fact[n-r], MOD-2, MOD) % MOD

p = comb(N*M-2, K-2)
ans = 0
for i in range(N):
    for j in range(M):
        if i == 0 and j == 0:
            continue
        d = i+j
        cnt = (N-i) * (M-j)
        if i != 0 and j != 0:
            cnt *= 2
        ans += d * cnt % MOD
ans = ans * p % MOD

print(ans)

Buggy python submission (verdict: Time Limit Exceeded):
N, M, K = map(int, input().split())

DIV = 10**9+7

def comb(l, r):
    if l == 0:
        return 1
    val = 1
    for i in range(r, r-l, -1):
        val *= i
    for i in range(l, 0, -1):
        val //= i
    return val

def calc_rec_num(N, M, xi, xj, yi, yj):
    cnt = 1
    cnt *= N - yi
    cnt *= M - yj
    # rotate
    if xi != yi and xj != yj:
        cnt *= 2
    return cnt


p = comb(K-2, N*M-2)
#print(K-2, N*M-2, p)
ans = 0
for i in range(N):
    for j in range(M):
        if i == 0 and j == 0:
            continue
        d = i+j
        #print(i, j, calc_rec_num(N, M, 0, 0, i, j))
        ans += d * calc_rec_num(N, M, 0, 0, i, j)
        #if ans > DIV:
        #    ans %= DIV
        #print(ans)

print((ans*p)%DIV)


Fixed submission:
from math import factorial
N, M, K = map(int, input().split())

MOD = 10**9+7

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

def comb(n, r):
    r = n-r if n-r < r else r
    return fact[n] * pow(fact[r], MOD-2, MOD) * pow(fact[n-r], MOD-2, MOD) % MOD

p = comb(N*M-2, K-2)
ans = 0
for i in range(N):
    for j in range(M):
        if i == 0 and j == 0:
            continue
        d = i+j
        cnt = (N-i) * (M-j)
        if i != 0 and j != 0:
            cnt *= 2
        ans += d * cnt % MOD
ans = ans * p % MOD

print(ans)

Buggy python submission (verdict: Time Limit Exceeded):
N, M, K = map(int, input().split())

DIV = 10**9+7

def comb(l, r):
    if l == 0:
        return 1
    val = 1
    for i in range(r, r-l, -1):
        val *= i
    for i in range(l, 0, -1):
        val //= i
    return val

def calc_rec_num(N, M, xi, xj, yi, yj):
    cnt = 1
    cnt *= N - yi
    cnt *= M - yj
    # rotate
    if xi != yi and xj != yj:
        cnt *= 2
    return cnt


p = comb(K-2, N*M-2)
#print(K-2, N*M-2, p)
ans = 0
for i in range(N):
    for j in range(M):
        if i == 0 and j == 0:
            continue
        d = i+j
        #print(i, j, calc_rec_num(N, M, 0, 0, i, j))
        ans += d * calc_rec_num(N, M, 0, 0, i, j)
        #if ans > DIV:
        #    ans %= DIV
        #print(ans)

print((ans*p)%DIV)


Fixed submission:
from math import factorial
N, M, K = map(int, input().split())

MOD = 10**9+7

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

def comb(n, r):
    r = n-r if n-r < r else r
    return fact[n] * pow(fact[r], MOD-2, MOD) * pow(fact[n-r], MOD-2, MOD) % MOD

p = comb(N*M-2, K-2)
ans = 0
for i in range(N):
    for j in range(M):
        if i == 0 and j == 0:
            continue
        d = i+j
        cnt = (N-i) * (M-j)
        if i != 0 and j != 0:
            cnt *= 2
        ans += d * cnt % MOD
ans = ans * p % MOD

print(ans)

Buggy python submission (verdict: Time Limit Exceeded):
N, M, K = map(int, input().split())

DIV = 10**9+7

def comb(l, r):
    if l == 0:
        return 1
    val = 1
    for i in range(r, r-l, -1):
        val *= i
    for i in range(l, 0, -1):
        val //= i
    return val

def calc_rec_num(N, M, xi, xj, yi, yj):
    cnt = 1
    cnt *= N - yi
    cnt *= M - yj
    # rotate
    if xi != yi and xj != yj:
        cnt *= 2
    return cnt


p = comb(K-2, N*M-2)
#print(K-2, N*M-2, p)
ans = 0
for i in range(N):
    for j in range(M):
        if i == 0 and j == 0:
            continue
        d = i+j
        #print(i, j, calc_rec_num(N, M, 0, 0, i, j))
        ans += d * calc_rec_num(N, M, 0, 0, i, j)
        if ans > DIV:
            ans %= DIV
        #print(ans)

print((ans*p)%DIV)


Fixed submission:
from math import factorial
N, M, K = map(int, input().split())

MOD = 10**9+7

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

def comb(n, r):
    r = n-r if n-r < r else r
    return fact[n] * pow(fact[r], MOD-2, MOD) * pow(fact[n-r], MOD-2, MOD) % MOD

p = comb(N*M-2, K-2)
ans = 0
for i in range(N):
    for j in range(M):
        if i == 0 and j == 0:
            continue
        d = i+j
        cnt = (N-i) * (M-j)
        if i != 0 and j != 0:
            cnt *= 2
        ans += d * cnt % MOD
ans = ans * p % MOD

print(ans)

Buggy python submission (verdict: Time Limit Exceeded):
N, M, K = map(int, input().split())

DIV = 10**9+7

def comb(l, r):
    if l == 0:
        return 1
    val = 1
    for i in range(r, r-l, -1):
        val *= i
    for i in range(l, 0, -1):
        val //= i
    return val

def calc_rec_num(N, M, xi, xj, yi, yj):
    cnt = 1
    cnt *= N - yi
    cnt *= M - yj
    # rotate
    if xi != yi and xj != yj:
        cnt *= 2
    return cnt


p = comb(K-2, N*M-2)
#print(K-2, N*M-2, p)
ans = 0
for i in range(N):
    for j in range(M):
        if i == 0 and j == 0:
            continue
        d = i+j
        #print(i, j, calc_rec_num(N, M, 0, 0, i, j))
        ans += d * calc_rec_num(N, M, 0, 0, i, j) * p
        if ans > DIV:
            ans %= DIV
        #print(ans)

print(ans)


Fixed submission:
from math import factorial
N, M, K = map(int, input().split())

MOD = 10**9+7

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

def comb(n, r):
    r = n-r if n-r < r else r
    return fact[n] * pow(fact[r], MOD-2, MOD) * pow(fact[n-r], MOD-2, MOD) % MOD

p = comb(N*M-2, K-2)
ans = 0
for i in range(N):
    for j in range(M):
        if i == 0 and j == 0:
            continue
        d = i+j
        cnt = (N-i) * (M-j)
        if i != 0 and j != 0:
            cnt *= 2
        ans += d * cnt % MOD
ans = ans * p % MOD

print(ans)

Buggy python submission (verdict: Runtime Error):
N, M, K = map(int, input().split())

DIV = 10**9+7

def comb(l, r):
    if l == 0:
        return 1
    val = 1
    for i in range(r, r-l, -1):
        val *= i
    for i in range(l, 0, -1):
        val /= i
    return val

def calc_rec_num(N, M, xi, xj, yi, yj):
    cnt = 0
    cnt += N - yi
    cnt += M - yj
    # rotate
    cnt *= 2
    return cnt


p = comb(K-2, N*M-2)
ans = 0
for i in range(N):
    for j in range(M):
        if i == 0 and j == 0:
            continue
        d = i+j
        ans += d * calc_rec_num(N, M, 0, 0, i, j) * p

print(ans % DIV)


Fixed submission:
from math import factorial
N, M, K = map(int, input().split())

MOD = 10**9+7

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

def comb(n, r):
    r = n-r if n-r < r else r
    return fact[n] * pow(fact[r], MOD-2, MOD) * pow(fact[n-r], MOD-2, MOD) % MOD

p = comb(N*M-2, K-2)
ans = 0
for i in range(N):
    for j in range(M):
        if i == 0 and j == 0:
            continue
        d = i+j
        cnt = (N-i) * (M-j)
        if i != 0 and j != 0:
            cnt *= 2
        ans += d * cnt % MOD
ans = ans * p % MOD

print(ans)