#include <bits/stdc++.h>
using namespace std;
long long powmod(long long a, long long b) {
  long long res = 1;
  if (a >= 1000000007) a %= 1000000007;
  for (; b; b >>= 1) {
    if (b & 1) res = res * a;
    if (res >= 1000000007) res %= 1000000007;
    a = a * a;
    if (a >= 1000000007) a %= 1000000007;
  }
  return res;
}
long long gcd(long long a, long long b) { return b == 0 ? a : gcd(b, a % b); }
int main() {
  int t;
  cin >> t;
  while (t--) {
    int n, m, k;
    cin >> n >> m >> k;
    int needed = 0;
    if (n % 2) {
      needed += m / 2;
      n--;
    }
    int col_count = 0;
    bool flag = true;
    while (n > 0 && needed < k) {
      if (col_count + 1 > (m / 2)) {
        flag = false;
        break;
      }
      needed += 2;
      col_count++;
      if (col_count == (m / 2)) {
        n -= 2;
        col_count = 0;
      }
    }
    if (needed != k || !flag) {
      cout << "NO" << endl;
      continue;
    } else {
      cout << "YES" << endl;
    }
  }
  return 0;
}
