// LUOGU_RID: 98929070
#include<bits/stdc++.h> 
using namespace std;
inline void solve() {
	int n,m,k;
	scanf("%d%d%d",&n,&m,&k);
	if(n%2==0&&m%2==1) {
		if(k>n*(m/2)) puts("NO");
		else {
			if(k%2==0) puts("YES");
			else puts("NO");	
		}
	}
	if(n%2==1&&m%2==0) {
		if(k<m/2) puts("NO");
		else {
			if((k-m/2)%2==0) puts("YES");
			else puts("NO");
		}
	}
	if(n%2==0&&m%2==0) {
		if(k%2==0) puts("YES");
		else puts("NO");
	}
}
signed main() {
	int T;
	scanf("%d",&T);
	while(T--) solve();
	return 0;
}