We have a grid of squares with N rows and M columns. Let (i, j) denote the square at the i-th row from the top and j-th column from the left. We will choose K of the squares and put a piece on each of them.

If we place the K pieces on squares (x_1, y_1), (x_2, y_2), ..., and (x_K, y_K), the cost of this arrangement is computed as:

\sum_{i=1}^{K-1} \sum_{j=i+1}^K (|x_i - x_j| + |y_i - y_j|)

Find the sum of the costs of all possible arrangements of the pieces. Since this value can be tremendous, print it modulo 10^9+7.

We consider two arrangements of the pieces different if and only if there is a square that contains a piece in one of the arrangements but not in the other.

Constraints

* 2 \leq N \times M \leq 2 \times 10^5
* 2 \leq K \leq N \times M
* All values in input are integers.

Input

Input is given from Standard Input in the following format:


N M K


Output

Print the sum of the costs of all possible arrangements of the pieces, modulo 10^9+7.

Examples

Input

2 2 2


Output

8


Input

4 5 4


Output

87210


Input

100 100 5000


Output

817260251
MOD = 10 ** 9 + 7

def mod_combination(n, k):
    def extended_gcd(a, b):
        if b == 0:
            return (a, 1, 0)
        d, x, y = extended_gcd(b, a % b)
        return (d, y, x - (a // b) * y)
    p, q = 1, 1
    for i in range(n - k + 1, n + 1):
        p = (p * i) % MOD
    for i in range(2, k + 1):
        q = (q * i) % MOD
    return p * (extended_gcd(q, MOD)[1] % MOD) % MOD

def mod_pow(a, b):
    return pow(a, b, MOD)


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

X = mod_pow(M, 2) * (mod_pow(N, 3) - N) % MOD
Y = mod_pow(N, 2) * (mod_pow(M, 3) - M) % MOD

comb = mod_combination(N * M - 2, K - 2)

ans = (X + Y) * mod_pow(6, MOD - 2) * comb % MOD

print(ans)
