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.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.util.ArrayList;
import java.util.StringTokenizer;


public class A {

	public static void main(String[] args) {
		FastScanner fs=new FastScanner();
		long n=fs.nextInt(), m=fs.nextInt(), k=fs.nextInt();
		if (n*m*2%k!=0) {
			System.out.println("NO");
		}
		else {
			long area=n*m*2/k;
			ArrayList<Integer> nFacts=allFacts((int)n*2);
			for (int i:nFacts) {
				if (area%i==0&&i<=n&&area/i<=m) {
					System.out.println("YES");
					System.out.println("0 0");
					System.out.println(i+" 0");
					System.out.println("0 "+(area/i));
					return;
				}
			}
			ArrayList<Integer> mFacts=allFacts((int)m*2);
			for (int i:mFacts) {
				if (area%i==0&&i<=m&&area/i<=n) {
					System.out.println("YES");
					System.out.println("0 0");
					System.out.println((area/i)+" 0");
					System.out.println("0 "+i);
					return;
				}
			}
			System.out.println("NO");
		}
	}
	
	static ArrayList<Integer> allFacts(int a) {
		ArrayList<Integer> toReturn=new ArrayList<>();
		for (int i=1; i*(long)i<=a; i++) {
			if (a%i==0) {
				toReturn.add(i);
				toReturn.add(a/i);
			}
		}
		return toReturn;
	}
	
	static class FastScanner {
		BufferedReader br=new BufferedReader(new InputStreamReader(System.in));
		StringTokenizer st=new StringTokenizer("");
		
		public String next() {
			while (!st.hasMoreElements())
				try {
					st=new StringTokenizer(br.readLine());
				} catch (IOException e) {
					e.printStackTrace();
				}
			return st.nextToken();
		}
		
		public int nextInt() {
			return Integer.parseInt(next());
		}
		
		public long nextLong() {
			return Long.parseLong(next());
		}
		
		public int[] readArray(int n) {
			int[] a=new int[n];
			for (int i=0; i<n; i++) {
				a[i]=nextInt();
			}
			return a;
		}
		
		public double nextDouble() {
			return Double.parseDouble(next());
		}
		
	}

}
