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 gcd(long long a, long long b) { return a ? gcd(b % a, a) : b; }
int main() {
  ios::sync_with_stdio(false);
  cin.tie();
  long long m, n, k;
  cin >> m >> n >> k;
  long long m0 = m, n0 = n;
  long long g1 = gcd(m, k);
  k /= g1;
  m /= g1;
  long long g2 = gcd(n, k);
  k /= g2;
  n /= g2;
  if (k == 1 || k == 2) {
    long long x = m, y = n;
    if (k == 1) {
      x *= 2;
      while (x > m0 || y > n0) {
        if (x > m0) {
          x /= 2;
          y *= 2;
        }
        if (y > n0) {
          x *= 2;
          y /= 2;
        }
      }
    }
    cout << "YES\n";
    cout << "0 0" << endl;
    cout << x << " 0" << endl;
    cout << "0 " << y << endl;
  } else {
    cout << "NO";
  }
  return 0;
}
