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.lang.reflect.Array;
import java.util.*;

import static java.lang.Math.*;

public class Main {
    long gcd(long a, long b) {
        if (b == 0) return a;
        return gcd(b, a % b);
    }

    void run() throws IOException {
        long n = nextLong();
        long m = nextLong();
        long k = nextLong();
        long n1 = n;
        long m1 = m;
        long k1 = k;
        long p = gcd(n1, k1);
        n1 /= p;
        k1 /= p;
        long r = gcd(m1, k1);
        m1 /= r;
        k1 /= r;
        if (k1 > 2) {
            pw.println("NO");
            pw.close();
            return;
        }
        if (k1 == 2) {
            pw.println("YES");
            pw.println(0 + " " + 0);
            pw.println(n1 + " " + 0);
            pw.println(0 + " " + m1);
        } else {
            pw.println("YES");
            if (n1 < n) {
                pw.println(0 + " " + 0);
                pw.println(n1 * 2 + " " + 0);
                pw.println(0 + " " + m1);
            } else {
                pw.println(0 + " " + 0);
                pw.println(n1 + " " + 0);
                pw.println(0 + " " + m1 * 2);
            }
        }
        pw.close();
    }

    class point implements Comparable<point> {
        int x;
        int col;

        public point(int a, int b) {
            x = a;
            col = b;
        }

        @Override
        public int compareTo(point o) {
            if (o.col == this.col) return Integer.compare(o.x, this.x);
            return -Integer.compare(o.col, this.col);
        }

    }

    long mod = (long) 1e9 + 7;
    BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
    //BufferedReader br = new BufferedReader(new FileReader("qual.in"));

    StringTokenizer st = new StringTokenizer("");
    PrintWriter pw = new PrintWriter(System.out);
    //PrintWriter pw = new PrintWriter("qual.out");

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

    String next() throws IOException {
        if (!st.hasMoreTokens()) {
            st = new StringTokenizer(br.readLine());
        }
        return st.nextToken();
    }

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

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

    public Main() throws FileNotFoundException {
    }

    public static void main(String[] args) throws IOException {
        new Main().run();
    }
}