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.io.*;
import java.util.*;

public class Drogon {
    public static void main(String[] args) throws Exception {
        FastReader sc = new FastReader();
        long n=sc.nextInt(),m=sc.nextInt(),k=sc.nextInt();
        if (2*m*n%k!=0){
            System.out.println("NO");
            return;
        }
        System.out.println("YES");
        if (k%2==0){
            k/=2;
            long k1=gcd(n,k),k2=k/k1;
            System.out.println("0 0");
            System.out.println("0 "+m/k2);
            System.out.println(n/k1+" 0");
            return;
        }
        long k1=gcd(n,k),k2=k/k1;
        long a=n/k1,b=m/k2;
        if (a<n)a*=2;
        else b*=2;
        System.out.println("0 0");
        System.out.println("0 "+b);
        System.out.println(a+" 0");

    }
    static long gcd(long a,long b){
        if (a==0)return b;
        return gcd(b%a,a);
    }
    static class FastReader {
        BufferedReader br;
        StringTokenizer st;

        public FastReader() {
            br = new BufferedReader(new
                    InputStreamReader(System.in));
        }

        String next() {
            while (st == null || !st.hasMoreElements()) {
                try {
                    st = new StringTokenizer(br.readLine());
                } catch (IOException e) {
                    e.printStackTrace();
                }
            }
            return st.nextToken();
        }

        int nextInt() {
            return Integer.parseInt(next());
        }

        long nextLong() {
            return Long.parseLong(next());
        }

        double nextDouble() {
            return Double.parseDouble(next());
        }

        String nextLine() {
            String str = "";
            try {
                str = br.readLine();
            } catch (IOException e) {
                e.printStackTrace();
            }
            return str;
        }
    }
}