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 int INF = 0x3f2f1f0f;
const long long LINF = 1ll * INF * INF;
long long gcd(long long a, long long b) {
  if (b == 0) return a;
  return gcd(b, a % b);
}
long long N, M, K;
int main() {
  cin >> N >> M >> K;
  long long all = 2 * N * M;
  if (all % K != 0) return puts("NO") < 0;
  all /= K;
  long long g = gcd(2 * N, K);
  long long x, y;
  if (g == 1) {
    x = N, y = all / x;
  } else {
    x = (2 * N / g), y = all / x;
  }
  printf("YES\n0 0\n%lld 0\n0 %lld\n", x, y);
  return 0;
}
