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.*;


public class HelloWorld{


public static long gcd(long a, long b) { 
    if (b == 0) return a; 
    return gcd(b, a % b);  
}
     public static void main(String []args){
        //System.out.println("Hello World");
        Scanner sc= new Scanner(System.in);
        long n=sc.nextLong(),m=sc.nextLong(),k=sc.nextLong();
        boolean isEven = (k%2==0);
        long p=n*m;
        if(isEven) k/=2;
        if(p%k!=0){System.out.print("NO");return;}
        long x = gcd(n, k);
	    k /= x;
	    long a = n / x;
	    x=gcd(m,k);
	    k/=x;
	    long b=m/x;
	    if(!isEven){
		    if(a < n)
			    a += a;
		    else{
			    assert(b < m);
		   	    b += b;
	    	}
	    }
	System.out.println("YES");
	System.out.println("0 0");
	System.out.println("0 "+b);
	System.out.println(a+" 0");
    }
}