Vasya has got three integers n, m and k. He'd like to find three integer points (x_1, y_1), (x_2, y_2), (x_3, y_3), such that 0 ≤ x_1, x_2, x_3 ≤ n, 0 ≤ y_1, y_2, y_3 ≤ m and the area of the triangle formed by these points is equal to nm/k.

Help Vasya! Find such points (if it's possible). If there are multiple solutions, print any of them.

Input

The single line contains three integers n, m, k (1≤ n, m ≤ 10^9, 2 ≤ k ≤ 10^9).

Output

If there are no such points, print "NO".

Otherwise print "YES" in the first line. The next three lines should contain integers x_i, y_i — coordinates of the points, one point per line. If there are multiple solutions, print any of them.

You can print each letter in any case (upper or lower).

Examples

Input

4 3 3


Output

YES
1 0
2 3
4 1


Input

4 4 7


Output

NO

Note

In the first example area of the triangle should be equal to nm/k = 4. The triangle mentioned in the output is pictured below: 

<image>

In the second example there is no triangle with area nm/k = 16/7.
#include <bits/stdc++.h>
using namespace std;
int main() {
  long long n, m, k;
  cin >> n >> m >> k;
  if ((2 * n * m) % k != 0) {
    cout << "NO" << endl;
    return 0;
  }
  cout << "YES" << endl;
  long long value = (2 * n * m) / k;
  for (long long i = max((value / max(n, m)), 1LL); i * i <= value; i++) {
    if (value % i == 0) {
      if (value / i <= n) {
        cout << 0 << " " << 0 << endl;
        cout << (value / i) << " " << 0 << endl;
        cout << 0 << " " << i << endl;
        return 0;
      }
      if (value / i <= m) {
        cout << 0 << " " << 0 << endl;
        cout << 0 << " " << (value / i) << endl;
        cout << i << " " << 0 << endl;
        return 0;
      }
    }
  }
}
