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 gc(long long a, long long b) {
  if (a == 0 || b == 0) {
    return a + b;
  }
  return gc(b % a, a);
}
int main() {
  ios_base::sync_with_stdio(false);
  cin.tie(0);
  long long n, m, k;
  cin >> n >> m >> k;
  if (k % 2LL == 0) {
    k /= 2LL;
    long long tmp = gc(k, n);
    n /= tmp;
    k /= tmp;
    tmp = gc(k, m);
    m /= tmp;
    k /= tmp;
    if (k > 1LL) {
      cout << "NO" << endl;
    } else {
      cout << "YES" << endl
           << "0 0" << endl
           << n << " " << 0 << endl
           << 0 << " " << m << endl;
    }
  } else {
    int flag = -1;
    long long tmp = gc(k, n);
    if (tmp > 1LL) {
      flag = 0;
    }
    k /= tmp;
    n /= tmp;
    tmp = gc(k, m);
    if (tmp > 1LL) {
      flag = 1;
    }
    k /= tmp;
    m /= tmp;
    if (flag == -1 || k > 1LL) {
      cout << "NO" << endl;
    } else {
      if (flag == 0) {
        n *= 2LL;
      } else {
        m *= 2LL;
      }
      cout << "YES" << endl
           << "0 0" << endl
           << n << " " << 0 << endl
           << 0 << " " << m << endl;
    }
  }
}
