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 n, m, k, l, aux, d, N, M;
long long cmmdc(long long a, long long b) {
  long long r;
  while (b) {
    r = a % b;
    a = b;
    b = r;
  }
  return a;
}
int main() {
  cin >> n >> m >> k;
  aux = 2;
  if (k % 2 == 0) {
    aux = 1;
    k /= 2;
  }
  N = n;
  M = m;
  d = cmmdc(n, k);
  n /= d;
  k /= d;
  d = cmmdc(m, k);
  m /= d;
  k /= d;
  if (k != 1) {
    cout << "NO\n";
    return 0;
  }
  if (n * aux <= N) {
    n *= aux;
    aux = 1;
  }
  if (m * aux <= M) {
    m *= aux;
    aux = 1;
  }
  if (aux != 1) {
    cout << "NO\n";
    return 0;
  }
  cout << "YES\n0 0\n0 " << m << '\n' << n << " 0\n";
  return 0;
}
