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;
#pragma warning(disable : 4996)
long long N, M, K;
long long gcd(long long a, long long b) {
  if (b == 0) return a;
  return gcd(b, a % b);
}
int main() {
  cin >> N >> M >> K;
  long long A = N * M, B = K;
  long long C = gcd(A, B);
  A /= C;
  B /= C;
  if (B >= 3)
    cout << "NO" << endl;
  else {
    long long V1 = K;
    long long V2 = gcd(V1, N);
    N /= V2;
    V1 /= V2;
    long long V3 = gcd(V1, M);
    M /= V3;
    V1 /= V3;
    if (B == 1) {
      if (V2 >= 2)
        N *= 2;
      else if (V3 >= 2)
        M *= 2;
    }
    cout << "YES" << endl;
    cout << "0 0 " << endl;
    cout << "0 " << M << endl;
    cout << N << " 0" << endl;
  }
  return 0;
}
