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>
void read(T &x) {
  x = 0;
  int f = 1;
  char ch = getchar();
  while (!isdigit(ch)) {
    if (ch == '-') f *= -1;
    ch = getchar();
  }
  while (isdigit(ch)) {
    x = x * 10 + ch - 48;
    ch = getchar();
  }
  x *= f;
}
long long a, b, k, re = 0;
long long gcd(long long a, long long b) { return b ? gcd(b, a % b) : a; }
int main() {
  read(a);
  read(b);
  read(k);
  if (k % 2 == 0)
    k /= 2;
  else
    re = 1;
  while (1) {
    long long d = max(gcd(k, a), gcd(k, b));
    if (d == 1) break;
    if (a % d == 0) {
      a /= d;
      k /= d;
      if (re) {
        a *= 2;
        re = 0;
      }
    } else {
      b /= d;
      k /= d;
      if (re) {
        b *= 2;
        re = 0;
      }
    }
  }
  if (k == 1) {
    cout << "YES" << endl;
    if (re)
      if (a < b)
        a *= 2;
      else
        b *= 2;
    cout << "0 0\n0 " << b << "\n" << a << " 0" << endl;
  } else {
    cout << "NO" << endl;
  }
  return 0;
}
