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;
void fail() {
  cout << "NO" << endl;
  exit(0);
}
int main() {
  long long i, j, k;
  long long N, M, K;
  cin >> N >> M >> K;
  if (K == 1 || N * M * 2 % K != 0) fail();
  long long A = N, B = M;
  bool done2 = false;
  if (K % 2 == 0) {
    K /= 2;
    done2 = true;
  }
  for (i = 2; i * i <= K; i++) {
    while (K % i == 0) {
      K /= i;
      if (A % i == 0) {
        A /= i;
      } else {
        B /= i;
      }
    }
  }
  if (K > 1) {
    if (A % K == 0) {
      A /= K;
    } else {
      B /= K;
    }
  }
  if (!done2) {
    if (2 * A <= N) {
      A *= 2;
    } else {
      B *= 2;
    }
  }
  cout << "YES" << endl;
  cout << 0 << " " << 0 << endl;
  cout << A << " " << 0 << endl;
  cout << 0 << " " << B << endl;
  return 0;
}
