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 n, m, K;
int main() {
  scanf("%d %d %d", &n, &m, &K);
  if (2LL * n * m % K) puts("NO"), exit(0);
  long long x = 2LL * n * m / K;
  puts("YES");
  printf("0 0\n");
  if (n < m) {
    int a = n, d = (x + a - 1) / a;
    int b = 1, c = 1LL * a * d - x;
    printf("%d %d\n%d %d\n", a, b, c, d);
  } else {
    int b = m, c = (x + b - 1) / b;
    int a = 1, d = 1LL * b * c - x;
    printf("%d %d\n%d %d\n", a, b, c, d);
  }
  return 0;
}
