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, c;
long long gcd(long long da, long long db) {
  if (da < db) {
    long long temp = da;
    da = db;
    db = temp;
  }
  if (!db)
    return da;
  else
    return gcd(db, da % db);
}
int main() {
  cin >> n >> m >> k;
  gcd(n, k);
  c = n * m;
  if (2 * c % k) cout << "NO" << endl, exit(0);
  cout << "YES" << endl;
  long long a, b;
  if (k % 2 == 0) {
    k /= 2;
    long long gd = gcd(k, n);
    a = n / gd;
    k /= gd;
    b = m / k;
  } else {
    long long gd = gcd(k, n);
    a = n / gd;
    k /= gd;
    b = m / k;
    if (2 * a <= n)
      a *= 2;
    else if (2 * b <= m)
      b *= 2;
  }
  cout << 0 << " " << 0 << endl;
  cout << a << " " << 0 << endl;
  cout << 0 << " " << b << endl;
  return 0;
}
