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;
template <typename T>
inline void ckmax(T& x, T y) {
  x = (y > x ? y : x);
}
template <typename T>
inline void ckmin(T& x, T y) {
  x = (y < x ? y : x);
}
long long n, m, K;
long long gcd(long long x, long long y) { return (!y) ? x : gcd(y, x % y); }
int main() {
  cin >> n >> m >> K;
  if (2 * n * m % K != 0) {
    cout << "NO" << endl;
    return 0;
  }
  if (K % 2 == 0) {
    K /= 2;
    long long x = gcd(n, K);
    n /= x;
    K /= x;
    assert(m % K == 0);
    m /= K;
    cout << "YES" << endl;
    cout << "0 0" << endl;
    cout << "0 " << m << endl;
    cout << n << " 0" << endl;
  } else {
    long long x = gcd(n, K);
    n /= x;
    K /= x;
    if (x == 1) {
      m *= 2;
    } else {
      n *= 2;
    }
    assert(m % K == 0);
    m /= K;
    cout << "YES" << endl;
    cout << "0 0" << endl;
    cout << "0 " << m << endl;
    cout << n << " 0" << endl;
  }
  return 0;
}
