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>
int main() {
  std::ios::sync_with_stdio(0);
  std::cin.tie(0);
  int n, m, k;
  std::cin >> n >> m >> k;
  if (k == 1 or n * (int64_t)m * 2 % k != 0) {
    std::cout << "NO\n";
    return 0;
  }
  int64_t cross = n * (int64_t)m * 2 / k;
  int x1, y1, x2, y2;
  x2 = n - ((cross - 1) % n + 1);
  y1 = 1;
  x1 = n;
  assert((cross + x2) % n == 0);
  y2 = (cross + x2) / n;
  assert(x1 * y2 - x2 * y1 == cross);
  assert(x1 <= n);
  assert(x2 <= n);
  assert(y1 <= m);
  assert(y2 <= m);
  std::cout << "YES\n0 0\n"
            << x1 << ' ' << y1 << '\n'
            << x2 << ' ' << y2 << '\n';
}
