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() {
  ios_base::sync_with_stdio(0);
  cin.tie(0);
  long long n, m, k, i;
  bool t = 0;
  cin >> n >> m >> k;
  if ((2 * m * n) % k > 0)
    cout << "NO";
  else {
    if (k == 2)
      cout << "YES\n0 0\n" << n << " 0\n0 " << m;
    else {
      k = (2 * m * n) / k;
      if (m >= n) {
        for (i = max(1, (int)(k / m)); i <= n; i++) {
          if (k % i == 0 && k / i <= m) {
            t = 1;
            break;
          }
        }
        if (!t)
          cout << "NO";
        else
          cout << "YES\n0 0\n" << i << " 0\n0 " << k / i;
      } else {
        for (i = max(1, (int)(k / n)); i <= m; i++) {
          if (k % i == 0 && k / i <= n) {
            t = 1;
            break;
          }
        }
        if (!t)
          cout << "NO";
        else
          cout << "YES\n0 0\n" << k / i << " 0\n0 " << i;
      }
    }
  }
  return 0;
}
