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 gcd(long long a, long long b) { return b == 0 ? a : gcd(b, a % b); }
int main() {
  long long n, m, k;
  scanf("%I64d%I64d%I64d", &n, &m, &k);
  if (2 * n * m % k) {
    printf("NO\n");
  } else {
    long long g = gcd(2 * n, k);
    long long x = 2 * n / g;
    long long y = m / (k / g);
    printf("YES\n");
    printf("0 0\n");
    if (x <= n && y <= m) {
      printf("%I64d 0\n", x);
      printf("0 %I64d\n", y);
    } else {
      x /= 2;
      y *= 2;
      printf("%I64d 0\n", x);
      printf("0 %I64d\n", y);
    }
  }
  return 0;
}
