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.Scanner;

public class vas_treug2 {
    static long gcd(long a,long b){
        if (b==0) {
            return a;
        }
        return gcd(b,a%b);
    }
    public static void main(String args[]){
        Scanner s = new Scanner(System.in);

        long n =s.nextLong();
        long m =s.nextLong();
        long k =s.nextLong();
        boolean del = false;
        if (2*m*n%k==0){
            if (k%2==0){
                del = true;
                k/=2;
            }
            long g = gcd(n,k);
            long k1 = k/g;
            long a = n/g;
            long b = m/k1;
            if (!del){
                if (a<n){
                    a*=2;
                } else {
                    b*=2;
                }
            }
            if (a==n){
                if (b>m){
                    System.out.println("NO");
                } else {
                    System.out.println("YES");
                    System.out.println(0+" "+0);
                    System.out.println(a+" "+0);
                    System.out.println(0+" "+b);
                }

            } else {
                System.out.println("YES");
                System.out.println(0+" "+0);
                System.out.println(a+" "+0);
                System.out.println(0+" "+b);
            }
        } else {
            System.out.println("NO");
        }
    }
}
