#include <bits/stdc++.h>
using namespace std;
const int N = 1000010;

int test,n,m,p,q;
long long s,ans,ss,k,z,tmp;

bool check(long long x,long long y,long long k){
    if (x>m||y>n) return 0;
    long long z=k-x-y*m+1+m;
    if (z&1LL) return 0;
    z/=2LL;
    if (z>1LL*n*m-1) return 0;
    int p,q;
    q=z%m;
    p=z/m;
    if (p+y<=n&&q+x<=m) return 1;
    return 0;
}
vector<long long> us;
long long fa[N];
int fb[N];
int na = 0;
void dfs(long long a, long long b, long long c), long long value) {
    if (a * b * c == value) {
        if (check(a, b, c))
        return ;
    }
}
int main(){
    scanf("%d",&test);
    while (test--){
        scanf("%d%d%I64d",&n,&m,&s);
        ans=1e15;
        s*=2LL;
        us.clear();
        na = 0;
        for (int i = 1;(long long)i * i <= s ; ++i)
        if (s % i == 0) {
            fa[na] =

            na++;
        }
        int sm = (int)us.size();
        for (int pi = 0; pi < sm; ++ pi){
            long long i = us[pi];
            ss=s/i;
                for (int pj=0; pj < sm; ++pj){
                    long long j = us[pj];
                    if (ss%j==0){
                        k=ss/j;
                        if (check(i,j,k)) ans=min(ans,1LL*i*j);
                        if (check(j,i,k)) ans=min(ans,1LL*i*j);
                        if (check(k,i,j)) ans=min(ans,1LL*i*k);
                        if (check(i,k,j)) ans=min(ans,1LL*i*k);
                        if (check(j,k,i)) ans=min(ans,1LL*k*j);
                        if (check(k,j,i)) ans=min(ans,1LL*k*j);
                    }
                }
            }
        if (ans==1e15) ans=-1;
        printf("%I64d\n",ans);

    }
}