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 GCD(int a, int b) {
  for (; b; a %= b, swap(a, b))
    ;
  return a;
}
int main() {
  ios_base::sync_with_stdio(false);
  cin.tie(NULL);
  cout.tie(NULL);
  ((void)0);
  ((void)0);
  int N, M, K;
  cin >> N >> M >> K;
  if ((2LL * N * M) % K) {
    cout << "NO\n";
  } else {
    int x = GCD(2 * N, K), y = GCD(2 * M, K);
    if (x > y) {
      K /= x;
      x = 2 * N / x;
      y = M / K;
      cout << "YES\n0 0\n0 " << y << '\n' << x << " 0\n";
    } else {
      K /= y;
      y = 2 * M / y;
      x = N / K;
      cout << "YES\n0 0\n0 " << y << '\n' << x << " 0\n";
    }
  }
  return 0;
}
