decomposition

#include <iostream>

int f (int M, int N, int k, int m, int n) {

    if (k == 1)
        return (M < m || (M == m && N <= n)) ? 1 : 0;

    int count = 0, new_m = 0, new_n = 0;
    while ((new_m < m || (new_m == m && new_n <= n)) && new_m <= M) {
        count += f(M - new_m, N - new_n, k - 1, new_m, new_n);

        if (new_n == N) {
            new_n = 0;
            ++new_m;
        }
        else {
            ++new_n;
        }
    }

    return count;
}

int res (int M, int N, int k) {
    return f(M, N, k, M, N);
}

int main() {
    int M, N, k;
    std::cin >> M >> N >> k;
    std::cout << res(M, N, k);
    return 0;
}