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 main() {
  long long n, m, k;
  cin >> n >> m >> k;
  if (2 * n * m % k != 0) {
    cout << "NO\n";
    return 0;
  }
  long long ansn = n * 2, ansm = m;
  for (long long i = 2; i < 500000; i++) {
    while (k % i == 0) {
      k /= i;
      if (ansn % i == 0)
        ansn /= i;
      else if (ansm % i == 0)
        ansm /= i;
      else
        assert(0);
    }
  }
  if (k != 1) {
    if (ansn % k == 0)
      ansn /= k;
    else if (ansm % k == 0)
      ansm /= k;
    else
      assert(0);
  }
  if (ansn > n) {
    assert(ansn % 2 == 0);
    ansn /= 2;
    ansm *= 2;
  }
  assert(ansn <= n && ansm <= m);
  cout << "YES\n";
  cout << "0 0\n";
  cout << ansn << " 0\n";
  cout << "0 " << ansm << "\n";
  return 0;
}
