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.
import java.util.*;
import java.io.*;
import java.lang.*;
import java.math.*;
public class A {
    public static void main(String[] args) throws Exception {
        BufferedReader bf = new BufferedReader(new InputStreamReader(System.in));
        // Scanner scan = new Scanner(System.in);
        PrintWriter out = new PrintWriter(new OutputStreamWriter(System.out));
        // int n = Integer.parseInt(bf.readLine());
        StringTokenizer st = new StringTokenizer(bf.readLine());
        // int[] a = new int[n]; for(int i=0; i<n; i++) a[i] = Integer.parseInt(st.nextToken());
        int n = Integer.parseInt(st.nextToken());
        int m = Integer.parseInt(st.nextToken());
        int k = Integer.parseInt(st.nextToken());

        if(2L*m*n % (0L + k) != 0L) {
          out.println("NO");
        }
        else {
          long area = 2L*m*n/k;
          int val = gcd(m, k);
          m /= val;
          k /= val;
          int val2 = gcd(n, k);
          n /= val2;
          k /= val2;
          if(k == 1) {
            if(val >= 2) m *= 2;
            else n *= 2;
          }
          out.println("YES");
          out.println("0 0");
          out.println(n + " " + 0);
          out.println(0 + " " + m);
        }



        // int n = scan.nextInt();

        out.close(); System.exit(0);
    }
    public static int gcd(int a, int b) {
       if (b==0) return a;
       return gcd(b, a%b);
    }
}
