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;
unsigned long long gcd(unsigned long long a, unsigned long long b) {
  while (a != 0 && b != 0) {
    if (a > b) {
      a %= b;
    } else {
      b %= a;
    }
  }
  return a + b;
}
int main() {
  unsigned long long n, m, k;
  cin >> n >> m >> k;
  unsigned long long n_ = n, m_ = m, k_ = k;
  if (2 * n * m % k == 0) {
    bool f = false;
    if (k % 2 == 0) {
      k /= 2;
      f = true;
    }
    unsigned long long a = gcd(n, k);
    n /= a;
    k /= a;
    m /= k;
    cout << "YES\n";
    cout << "0 0\n";
    if (!f) {
      if (n * 2 <= n_) {
        cout << n * 2 << " 0"
             << "\n";
        cout << "0 " << m;
      } else {
        cout << n << " 0"
             << "\n";
        cout << "0 " << m * 2;
      }
    } else {
      cout << n << " 0\n";
      cout << "0 " << m;
    }
  } else {
    cout << "NO";
  }
  return 0;
}
