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;
void check(long long x, long long y) {
  if (x <= n && y <= m) {
    cout << "YES\n";
    cout << 0 << " " << 0 << "\n";
    cout << x << " " << 0 << "\n";
    cout << 0 << " " << y << "\n";
    exit(0);
  }
}
int main() {
  ios_base::sync_with_stdio(false);
  cin.tie(0);
  cout.tie(0);
  cin >> n >> m >> k;
  long long X = 2 * n * m;
  if (X % k != 0) {
    cout << "NO";
    return 0;
  }
  X /= k;
  for (int i = 1; i <= sqrt(n); i++) {
    if (n % i == 0) {
      long long x = i;
      long long y = X / x;
      if (X % x == 0) {
        check(x, y);
        check(y, x);
      }
      x = n / i;
      y = X / x;
      if (X % x == 0) {
        check(x, y);
        check(y, x);
      }
    }
  }
  for (int i = 1; i <= sqrt(m); i++) {
    if (m % i == 0) {
      long long x = i;
      long long y = X / i;
      if (X % x == 0) {
        check(x, y);
        check(y, x);
      }
      x = m / i;
      y = X / x;
      if (X % x == 0) {
        check(x, y);
        check(y, x);
      }
    }
  }
  cout << "NO";
  return 0;
}
