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 int gcd(long long int a, long long int b) {
  if (a == 0) return b;
  return gcd(b % a, a);
}
int main() {
  ios_base::sync_with_stdio(false);
  cin.tie(NULL);
  cout.tie(NULL);
  long long int n, m, k;
  cin >> n >> m >> k;
  long long int a = n * m, b = k;
  long long int g = gcd(a, b);
  a /= g;
  b /= g;
  if (b > 2) {
    cout << "NO" << endl;
  } else if (b == 2) {
    cout << "YES" << endl;
    cout << "0 0" << endl;
    long long int tmp = gcd(n, g);
    cout << "0 " << m * tmp / g << endl;
    cout << n / tmp << " 0" << endl;
  } else if (k == 1) {
    cout << "NO" << endl;
  } else {
    cout << "YES" << endl;
    cout << "0 0" << endl;
    long long int k1 = gcd(n, k);
    long long int k2 = k / k1;
    if (k1 > 1) {
      cout << 2 * n / k1 << " 0" << endl;
      cout << "0 " << m / k2 << endl;
    } else {
      cout << n / k1 << " 0" << endl;
      cout << "0 " << 2 * m / k2 << endl;
    }
  }
}
