import std.stdio, std.array, std.string, std.conv, std.algorithm;
import std.typecons, std.range, std.random, std.math, std.container;
import std.numeric, std.bigint, core.bitop, core.stdc.string;

immutable long MOD = 10^^9 + 7;

void main() {
    auto s = readln.split.map!(to!int);
    auto N = s[0];
    auto M = s[1];
    auto K = s[2];

    long C = 1;
    foreach (i; 1..N*M-1) {
        C = C * i % MOD;
    }
    foreach (i; 1..K-1) {
        C = C * powmod(i, MOD-2, MOD) % MOD;
    }
    foreach (i; 1..(N*M-2-(K-2))+1) {
        C = C * powmod(i, MOD-2, MOD) % MOD;
    }

    long ans = 0;
    long tmp = 0;

    foreach (i; 0..N) {
        long right = N - i - 1;
        long left = i;
        tmp = (tmp + right * (right + 1) / 2 * M) % MOD;
        tmp = (tmp + left * (left + 1) / 2 * M) % MOD;
    }

    ans += tmp * C % MOD * M % MOD;
    ans %= MOD;

    tmp = 0;
    foreach (i; 0..M) {
        long right = M - i - 1;
        long left = i;
        tmp = (tmp + right * (right + 1) / 2 * N) % MOD;
        tmp = (tmp + left * (left + 1) / 2 * N) % MOD;
    }

    ans += tmp * C % MOD * N % MOD;
    ans %= MOD;
    ans =  ans * powmod(2, MOD-2, MOD) % MOD;
    ans.writeln;
}

long powmod(long a, long x, long m) {
    long ret = 1;
    while (x) {
        if (x % 2) ret = ret * a % m;
        a = a * a % m;
        x /= 2;
    }
    return ret;
}
