Lares - Them divide c people into t groups

There is m men, and n women.The boss chooses k people. Them divide m+n-k remain people into t groups, each group exactly 2 men and 1 woman. Find max(t)

For example:
Input
264936043 821529140 438045170
Ouput
132468021

#include <iostream>

using namespace std;

int n, m, k, res, t;

int main(){
    cin >> n >> m >> k;
    for (int i = max(k-m, 0); i <= n; i++){
        res =  max(res, min((n-i)/2, m-k+i));
    }
    cout << res;
}

My code is TLE.

I think the number of men chosen is (n+2k-2m)/3 because (n-i) ~ 2*(m-k+i), but it is not correct.