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;
const long long pm = 10e9 + 7;
const long long inf = 400000000000000000;
long long gcd(long long a, long long b) {
  if (a < b) return gcd(b, a);
  long long c = a % b;
  if (c) {
    return gcd(b, c);
  } else
    return b;
}
int main() {
  long long n, m, k;
  cin >> n >> m >> k;
  if (2 * n * m % k != 0) {
    cout << "NO\n";
  } else {
    cout << "YES" << endl;
    long long g = gcd(2 * n, k);
    if (g == 1) {
      long long x = n;
      long long y = (2 * m) / (k);
      cout << "0 0\n";
      cout << x << " 0\n";
      cout << "0 " << y << endl;
    } else {
      long long x = 2 * n / g;
      long long y = (2 * n * m) / (x * k);
      if (x > n || y > m) {
        long long tmp = x;
        x = y;
        y = tmp;
      }
      cout << "0 0\n";
      cout << x << " 0\n";
      cout << "0 " << y << endl;
    }
  }
  return 0;
}
