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;
int64_t gcd(int x, int y) {
  while (y != 0) {
    int64_t t = y;
    y = x % y;
    x = t;
  }
  return x;
}
int main() {
  int64_t n, m, k, n1, m1, k1, g1, g2;
  cin >> n >> m >> k;
  if ((2 * n * m) % k == 0) {
    g1 = gcd(n, k);
    g2 = gcd(m, k);
    if (k % 2 == 0) {
      k1 = k / 2;
      n1 = n / gcd(n, k1);
      assert(n1 <= n);
      m1 = (n * m) / (n1 * k1);
      assert(m1 <= m);
    } else if (g1 != 1) {
      assert(g1 >= 3);
      n1 = (2 * n) / g1;
      assert(n1 <= n);
      m1 = (2 * n * m) / (k * n1);
      assert(m1 <= m);
    } else {
      assert(g2 >= 3);
      m1 = (2 * m) / g2;
      assert(m1 <= m);
      n1 = (2 * n * m) / (k * m1);
      assert(n1 <= n);
    }
    assert(n1 * m1 == (2 * n * m) / k);
    cout << "YES\n";
    cout << "0 0\n";
    cout << n1 << " 0\n";
    cout << "0 " << m1 << "\n";
  } else {
    cout << "NO";
  }
  return 0;
}
