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() {
  ios_base::sync_with_stdio(false);
  cin.tie(NULL);
  cout.tie(NULL);
  long long n, m, k;
  cin >> n >> m >> k;
  long long t = 2 * n * m;
  if (t % k == 0) {
    long long x = t / k;
    long long p = 0, q = 0;
    if (n % k == 0) {
      p = 2 * n / k, q = m;
    } else if (m % k == 0) {
      p = n, q = 2 * m / k;
    } else if (k == 2) {
      p = n, q = m;
    } else {
      for (long long i = 1; i * i <= x; i++) {
        if (x % i == 0) {
          if (i <= n && (x / i) <= m) {
            p = i;
            q = x / i;
            break;
          } else if (i <= m && (x / i) <= n) {
            p = x / i;
            q = i;
            break;
          }
        }
      }
    }
    cout << "YES\n";
    cout << "0 0\n";
    cout << p << " 0\n";
    cout << "0 " << q << "\n";
  } else {
    cout << "NO\n";
  }
  return 0;
}
