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 ll = long long;
ll gcd(ll a, ll b) {
  ll t;
  while (b != 0) {
    t = a % b;
    a = b;
    b = t;
  }
  return a;
}
int main(int argc, char *argv[]) {
  ll n, m, k;
  std::cin >> n >> m >> k;
  if (2 * n * m % k) {
    std::cout << "NO\n";
    exit(0);
  }
  ll area = 2 * n * m / k;
  ll x = gcd(k, 2 * n);
  if (x == 1) {
    std::cout << "YES\n0 0\n" << n << " 0\n0 " << m * 2 / k << '\n';
  } else {
    std::cout << "YES\n0 0\n" << n * 2 / x << " 0\n0 " << m * x / k << '\n';
  }
}
