CF1551D1

// Problem: D1. Domino (easy version)
// Contest: Codeforces - Codeforces Round 734 (Div. 3)
// URL: https://codeforces.com/problemset/problem/1551/D1
// Memory Limit: 256 MB
// Time Limit: 1000 ms
//
// Powered by CP Editor (https://cpeditor.org)

#include <assert.h>
#include <bits/stdc++.h>
using namespace std;
#ifndef __DEBUG__
#define dbg(...) 42
#endif
template <class T> using mpq = priority_queue<T, vector<T>, greater<T>>;

using ll = long long;
using a2l = array<ll, 2>;
using pll = pair<ll, ll>;
using vl = vector<ll>;

void solve_wa()
{
    ll n, m, k;
    cin >> n >> m >> k;
    ll all = n * m;
    if (m % 2 == 0 && n % 2 == 0) {
        cout << (k % 2 == 0 ? "YES" : "NO") << '\n';
        return;
    }
    if (n % 2) {
        all -= m;
        cout << (k * 2 % (2 * m) == 0 ? "YES" : "NO") << '\n';
        return;
    }
    cout << (k * 2 % (2 * m) == m ? "YES" : "NO") << '\n';
}

void solve()
{
    ll n, m, k;
    cin >> n >> m >> k;
    if (m % 2 == 0 && n % 2 == 0) {
        cout << (k % 2 == 0 ? "YES" : "NO") << '\n';
        return;
    }

    ll all = n * m / 2;
    if (n % 2) {
        k -= m / 2;
        all -= m / 2;
    } else {
        all -= n / 2;
    }
    cout << (all >= k && k >= 0 && k % 2 == 0 ? "YES" : "NO") << '\n';
}

int main(int argc, char **argv)
{
    ll t;
    cin >> t;
    while (t--)
        solve();
    return 0;
};