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;
  bool odd = true;
  if ((n * m * 2 % k > 0) || (k < 2)) {
    cout << "NO";
  } else {
    long long a = n;
    long long b = m;
    long long l = k;
    if (l % 2 == 0) {
      l /= 2;
      odd = false;
    }
    for (long long i = 2; i <= (k); i++) {
      if (l % i == 0) {
        do {
          l /= i;
          if (n % i == 0) {
            n /= i;
          } else {
            m /= i;
          }
        } while (l % i == 0);
      }
      if ((n % l == 0) && (l != 1)) {
        n /= l;
        break;
      } else {
        if ((m % l == 0) && (l != 1)) {
          m /= l;
          break;
        }
      }
      if (l == 1) {
        break;
      }
    }
    if (odd) {
      if (2 * n <= a) {
        n *= 2;
      } else {
        m *= 2;
      }
    }
    cout << "YES" << endl;
    cout << "0 0" << endl;
    cout << "0 " << m << endl;
    cout << n << " 0";
  }
  return 0;
}
