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, x1, y11, x2, y2, x3, y3, ma;
long long ans, l;
int main() {
  cin >> n >> m >> k;
  ans = (long long)n * m * 2;
  if (ans % k) {
    puts("NO");
    return 0;
  }
  ans /= k;
  x2 = y11 = 0;
  x3 = y3 = 0;
  ma = max(n, m);
  for (int i = max(1ll, ans / ma); (long long)i * i <= ans && (i <= ma); ++i) {
    if (ans % i == 0) {
      l = ans / i;
      if (l > ma) continue;
      if (i <= n && l <= m) {
        x1 = i, y2 = l;
        cout << "YES" << endl;
        cout << x1 << " " << y11 << endl;
        cout << x2 << " " << y2 << endl;
        cout << x3 << " " << y3 << endl;
        return 0;
      }
      if (i <= m && l <= n) {
        y2 = i, x1 = l;
        cout << "YES" << endl;
        cout << x1 << " " << y11 << endl;
        cout << x2 << " " << y2 << endl;
        cout << x3 << " " << y3 << endl;
        return 0;
      }
    }
  }
  puts("NO");
  return 0;
}
