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 maxn = 1e6 + 5, base = 11;
long long gcd(long long first, long long second) {
  while (second) first %= second, swap(first, second);
  return first;
}
int main() {
  ios::sync_with_stdio(false), cin.tie(0);
  long long n, m, k;
  cin >> n >> m >> k;
  long long K = k;
  if (K % 2 == 0) k = k / 2;
  if ((m * n) % k != 0) {
    cout << "NO\n";
    return 0;
  }
  long long g = gcd(k, n);
  k = k / g;
  long long first = n / g;
  g = gcd(k, m);
  k = k / g;
  long long second = m / g;
  if (K % 2 != 0) (first < n) ? first *= 2 : second *= 2;
  if ((first * second) / 2 != (m * n) / K) {
    if (first % 2 == 0)
      first /= 2;
    else if (second % 2 == 0)
      second /= 2;
  }
  cout << "YES\n"
       << "0 0\n"
       << first << " 0\n"
       << "0 " << second << "\n";
  return 0;
}
