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 a, b, k;
int main() {
  cin >> a >> b >> k;
  long long A, B;
  A = a;
  B = b;
  for (int i = 2; i * i <= k; i++) {
    while ((k % i == 0) && (a % i == 0)) {
      k /= i;
      a /= i;
    }
    while ((k % i == 0) && (b % i == 0)) {
      k /= i;
      b /= i;
    }
    if (k % i == 0) {
      long long ii = k / i;
      if (ii == 1) continue;
      while ((k % ii == 0) && (a % ii == 0)) {
        k /= ii;
        a /= ii;
      }
      while ((k % ii == 0) && (b % ii == 0)) {
        k /= ii;
        b /= ii;
      }
    }
  }
  if (a % k == 0) {
    a /= k;
    k = 1;
  }
  if (b % k == 0) {
    b /= k;
    k = 1;
  }
  if (k % a == 0) {
    k /= a;
    a /= a;
  }
  if (k % b == 0) {
    k /= b;
    b /= b;
  }
  if (k == 2) {
    k = 1;
  } else if (k == 1) {
    if (a < A) {
      a *= 2;
    } else if (b < B) {
      b *= 2;
    } else {
      k = 2;
    }
  }
  if (k == 1) {
    puts("YES");
    cout << 0 << " " << 0 << endl;
    cout << a << " " << 0 << endl;
    cout << 0 << " " << b << endl;
  } else {
    puts("NO");
  }
  return 0;
}
