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;
long long gcd(long long a, long long b) {
  if (a % b == 0) return b;
  return gcd(b, a % b);
}
int main() {
  while (cin >> n >> m >> k) {
    long long h, w;
    long long g;
    if ((m * n * 2) % k != 0)
      puts("NO");
    else {
      puts("YES");
      puts("0 0");
      h = m, w = n;
      if (k % 2 == 0) {
        k /= 2;
        g = gcd(k, h);
        h /= g;
        k /= g;
        g = gcd(k, w);
        w /= g;
      } else {
        g = gcd(k, m);
        if (g > 1) {
          k /= g;
          h = h / g * 2;
          g = gcd(k, n);
          w /= g;
        } else {
          g = gcd(k, n);
          w = w / g * 2;
        }
      }
      printf("0 %lld\n", h);
      printf("%lld 0\n", w);
    }
  }
  return 0;
}
