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 vas3 {
    public static void main( String[] args ) {
	Scanner in = new Scanner( System.in );
	long n = in.nextLong(), m = in.nextLong(), k = in.nextLong();
	if ( ( 2 * n * m / k ) * k != 2 * n * m )
	    System.out.println( "NO" );
	else {
	    System.out.println( "YES" );
	    System.out.println( "0 0" );
	    long g, a, b;
	    if ( k % 2 == 0 ) {
	 	g = gcd ( n, k / 2 );
		a = n / g;
		b = 2 * m * g / k;
	    }
	    else {
		g = gcd ( n, k );
		a = n / g;
		b = m * g / k;
		if ( g > 1 )
		    a *= 2;
		else
		    b *= 2;
	    }
	    System.out.println( a + " 0" );
	    System.out.println( "0 " + b );
	}
    }

    // a <= b
    static long gcd ( long a, long b ) {
	if ( a == 0 )
	    return b;
	b %= a;
	return gcd ( Math.min( a, b ), Math.max( a, b ) );
    }
}
