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 flag = false;
  if ((n * m) % k != 0 && k % 2 != 0) {
    cout << "NO";
    return 0;
  }
  if ((n * m) % k != 0 && k % 2 == 0) {
    flag = true;
    k /= 2;
    if ((n * m) % k != 0) {
      cout << "NO";
      return 0;
    }
  }
  long long n2 = n, m2 = m, k2 = k;
  for (long long i = 2; i <= sqrt(k2); i++) {
    while (k2 % i == 0) {
      if (n2 % i == 0) {
        n2 /= i;
      } else {
        m2 /= i;
      }
      k2 /= i;
    }
  }
  if (k2 > 1) {
    if (n2 % k2 == 0) {
      n2 /= k2;
    } else {
      m2 /= k2;
    }
  }
  if (!flag) {
    if (n2 < n) {
      n2 *= 2;
    } else {
      m2 *= 2;
    }
  }
  cout << "YES\n";
  cout << "0 0\n0 " << m2 << "\n" << n2 << " 0\n";
}
