#include <fstream>
#include <algorithm>
using namespace std;
typedef long long ll;
ifstream in("Cheerleaders.in");
ofstream out("Cheerleaders.out");
int n,m,K,hot;
ll ans=0;
ll mod=1000007;
ll CO[505][505]={0};
void Cmaker()
{
	int i,j;
	CO[1][1]=1;
	CO[1][0]=1;
	for(i=2;i<=500;i++)
	{
		CO[i][0]=1;
		for(j=1;j<=i;j++)
		{
			CO[i][j]=CO[i-1][j]+CO[i-1][j-1];
			CO[i][j]%=mod;
		}
	}
}
ll C(int n,int m)
{
	if(m<0||m>n||n<=0)return 0;
	else return CO[n][m];
}
void read()
{
	in>>n>>m>>K;
	hot=n*m;
}
ll work()
{
	ll tot=0;
	out<<tot<<endl;
	tot+=C(hot-8,K-4);//0
	out<<tot<<endl;
	tot+=C(hot-6,K-3)*4;//1
	out<<tot<<endl;
	tot+=C(hot-4,K-2)*2;//2
	out<<tot<<endl;
	tot+=C(hot-5,K-3)*4;//2
	out<<tot<<endl;
	
	tot+=C(hot-4,K-3)*4;//3
	out<<tot<<endl;
	tot+=C(hot-4,K-4);//4
	out<<tot<<endl;
	
	return tot;
}
int main()
{
	int i,T;
	
	Cmaker();
    //out<<C(6,0)<<endl;
	in>>T;
	while(T--)
	{
		read();
		out<<work()<<endl;
	}
	return 0;
}