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>
#pragma GCC optimize("O3")
#pragma GCC target("sse4")
using namespace std;
template <class T>
T gcd(T a, T b) {
  return ((b == 0) ? a : gcd(b, a % b));
}
int main() {
  ios_base::sync_with_stdio(false);
  cin.tie(0);
  long long n, m, k, k1;
  cin >> n >> m >> k;
  k1 = k;
  if (((2 * n * m) % k != 0)) {
    cout << "NO" << endl;
    return 0;
  }
  long long a = 2 * m, b = n;
  for (long long i = 2; (i * i) <= k; i++) {
    while (k % i == 0) {
      if (a % i == 0)
        a /= i;
      else
        b /= i;
      k /= i;
    }
  }
  if (k > 1) {
    if (a % k == 0)
      a /= k;
    else
      b /= k;
  }
  if (a > m) {
    a = m, b = 2 * n;
    k = k1;
    for (long long i = 2; (i * i) <= k; i++) {
      while (k % i == 0) {
        if (b % i == 0)
          b /= i;
        else
          a /= i;
        k /= i;
      }
    }
    if (k > 1) {
      if (b % k == 0)
        b /= k;
      else
        a /= k;
    }
    cout << "YES" << endl;
    cout << "0 0" << endl;
    cout << 0 << " " << a << endl;
    cout << b << " " << 0 << endl;
  } else {
    cout << "YES" << endl;
    cout << "0 0" << endl;
    cout << 0 << " " << a << endl;
    cout << b << " " << 0 << endl;
  }
  return 0;
}
