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 n, m, k;
long long dc(long long x, long long y) {
  long long r;
  while (y) {
    r = x % y;
    x = y;
    y = r;
  }
  return x;
}
int main() {
  cin >> n >> m >> k;
  if (2 * n * m % k != 0)
    cout << "NO";
  else {
    int ok = 0;
    cout << "YES" << '\n';
    if (k % 2 == 0) {
      k = k / 2;
      ok = 1;
    }
    long long d = dc(n, k);
    k = k / d;
    long long x = n / d;
    d = dc(m, k);
    k = k / d;
    long long y = m / d;
    if (ok) {
      cout << 0 << " " << 0 << '\n';
      cout << x << " " << 0 << '\n';
      cout << 0 << " " << y << '\n';
    } else {
      cout << 0 << " " << 0 << '\n';
      if (x < n)
        x *= 2;
      else if (y < m)
        y *= 2;
      cout << x << " " << 0 << '\n';
      cout << 0 << " " << y << '\n';
    }
  }
}
