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;
long long n, m, k;
int main() {
  ios::sync_with_stdio(false);
  cin.tie(0);
  cin >> n >> m >> k;
  long long t1 = n, t2 = m;
  bool flag = false;
  if (k & 1)
    flag = true;
  else
    k /= 2;
  for (int i = 2; i <= sqrt(k); i++) {
    if (k % i == 0) {
      if (n % i == 0) {
        k /= i;
        n /= i;
      } else if (m % i == 0) {
        k /= i;
        m /= i;
      } else {
        return cout << "NO\n", 0;
      }
      i--;
    }
  }
  if (k != 1) {
    if (n % k == 0) {
      n /= k;
    } else if (m % k == 0) {
      m /= k;
    } else {
      return cout << "NO\n", 0;
    }
  }
  if (flag) {
    if (n * 2 <= t1)
      n *= 2;
    else if (m * 2 <= t2)
      m *= 2;
    else
      return cout << "NO\n", 0;
  }
  cout << "YES\n0 0\n0 " << m << "\n" << n << " 0\n";
  return 0;
}
