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.
// package contests.CF1053;

import java.io.*;
import java.util.Arrays;
import java.util.StringTokenizer;

public class A {
    public static void main(String[] args) throws IOException {
        Scanner sc = new Scanner(System.in);
        long n = sc.nextInt();
        long m = sc.nextInt();
        long k = sc.nextInt();
        if(2*m*n % k != 0)
        {
            System.out.println("NO");
            return;
        }
        double[] sides = new double[3];
        StringBuilder sb = new StringBuilder();
        sb.append("YES\n");
        if((2*n)%k  == 0){
            sb.append("0 0\n");
            sb.append(2*n/k + " 0\n");
            sb.append(n/k + " " + m);
        }else if(2*m % k == 0){
            sb.append("0 0\n");
            sb.append(0 + " " + 2*m/k + "\n");
            sb.append(n + " " + m/k);
        }else {
            long y = m/gcd(m, k);
            k /= gcd(m, k);
            long x = 2*n/k;
            sb.append("0 0\n");
            sb.append(x + " 0\n");
            sb.append("0 " + y);
        }

        System.out.println(sb);
    }

    /*
    sides[0] = dist(0, 2*m/k, 0, 0);
            sides[1] = dist(0, 2*m/k, n, m/k);
            sides[2] = dist(n, m/k, 0, 0);
     */
    static double dist(long x1, long y1, long x2, long y2){
        long dx = (x2-x1);
        long dy = (y2-y1);
        return Math.sqrt(dx*dx + dy*dy);
    }

    static long gcd(long a, long b){
        return b==0?a:gcd(b, a%b);
    }

    static class Scanner
    {
        StringTokenizer st; BufferedReader br;
        public Scanner(InputStream s){	br = new BufferedReader(new InputStreamReader(s));}
        public Scanner(java.lang.String s) throws FileNotFoundException {	br = new BufferedReader(new FileReader(new File(s)));}
        public java.lang.String next() throws IOException {while (st == null || !st.hasMoreTokens()) st = new StringTokenizer(br.readLine());return st.nextToken();}
        public int nextInt() throws IOException {return Integer.parseInt(next());}
        public long nextLong() throws IOException {return Long.parseLong(next());}
        public java.lang.String nextLine() throws IOException {return br.readLine();}
        public boolean ready() throws IOException {return br.ready();}
    }
}
