There is a right triangle with legs of length a and b. Your task is to determine whether it is possible to locate the triangle on the plane in such a way that none of its sides is parallel to the coordinate axes. All the vertices must have integer coordinates. If there exists such a location, you have to output the appropriate coordinates of vertices.

Input

The first line contains two integers a, b (1 ≤ a, b ≤ 1000), separated by a single space.

Output

In the first line print either "YES" or "NO" (without the quotes) depending on whether the required location exists. If it does, print in the next three lines three pairs of integers — the coordinates of the triangle vertices, one pair per line. The coordinates must be integers, not exceeding 109 in their absolute value.

Examples

Input

1 1


Output

NO


Input

5 5


Output

YES
2 1
5 5
-2 4


Input

5 10


Output

YES
-10 4
-2 -2
1 2

// Problem : A. Triangle
// Contest : Codeforces - Codeforces Round #239 (Div. 1)
// URL : https://codeforces.com/problemset/problem/407/A
// Memory Limit : 256 MB
// Time Limit : 1000 ms
// Powered by CP Editor (https://github.com/cpeditor/cpeditor)

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

public class a implements Runnable{
	
    public static void main(String[] args) {
        new Thread(null, new a(), "process", 1<<26).start();
    }
	public void run() {
		FastReader scan = new FastReader();
        PrintWriter out = new PrintWriter(new OutputStreamWriter(System.out));
		//PrintWriter out = new PrintWriter("file.out");
		Task solver = new Task();
		//int t = scan.nextInt();
		int t = 1;
		for(int i = 1; i <= t; i++) solver.solve(i, scan, out);
		out.close();
	}

	static class Task {
		static final int inf = Integer.MAX_VALUE;

		public void solve(int testNumber, FastReader sc, PrintWriter pw) {
			//CHECK FOR QUICKSORT TLE
			//***********************//
			//CHECK FOR INT OVERFLOW
			//***********************//
			int n = sc.nextInt();
			int m = sc.nextInt();
			int x1=0, y1=0;
			int x2=0, y2=0;
			int k = gcd(n, m);
			if(k == 1) {
				pw.println("NO");
				return;
			}
			l:
			for(int i = 1; i <= 1000; i++) {
				for(int j = 1; j <= 1000; j++) {
					if(i * i + j * j == k * k) {
						x2 = i;
						y2 = j;
						break l;
					}
				}
			}
			if(x2 == 0 || y2 == 0 ) {
				pw.println("NO");
				return;
			}
			
			if(x2 * n == y2 * m) {
				pw.println("YES");
				pw.printf("%d %d%n%d %d%n%d %d%n", x1, y1, x2 * n/k, y2* n/k, -y2 * m/k, x2 * m/k);
				return;
			}
			if(x2 * m == y2 * n) {
				pw.println("YES");
				pw.printf("%d %d%n%d %d%n%d %d%n", x1, y1, y2* n/k, x2 * n/k, x2 * -m/k, y2 * m/k);
				return;
			}
			pw.println("YES");
			pw.printf("%d %d%n%d %d%n%d %d%n", x1, y1, x2 * n/k, y2* n/k, y2 * m/k, x2 * -m/k);
		}
		int gcd(int a, int b) {
			return a == 0 ? b : gcd(b%a, a);
		}
	}
	static long binpow(long a, long b, long m) {
		a %= m;
		long res = 1;
		while (b > 0) {
			if ((b & 1) == 1)
				res = res * a % m;
			a = a * a % m;
			b >>= 1;
		}
		return res;
	}
	static void sort(int[] x){
		shuffle(x);
		Arrays.sort(x);
	}
	static void sort(long[] x){
		shuffle(x);
		Arrays.sort(x);
	}
	static class tup implements Comparable<tup>{
		int a, b;
		tup(int a,int b){
			this.a=a;
			this.b=b;
		}
		@Override
		public int compareTo(tup o){
			return Integer.compare(o.b,b);
		}
	}
	static void shuffle(int[] a) {
		Random get = new Random();
		for (int i = 0; i < a.length; i++) {
			int r = get.nextInt(i + 1);
			int temp = a[i];
			a[i] = a[r];
			a[r] = temp;
		}
	}

	static void shuffle(long[] a) {
		Random get = new Random();
		for (int i = 0; i < a.length; i++) {
			int r = get.nextInt(i + 1);
			long temp = a[i];
			a[i] = a[r];
			a[r] = temp;
		}
	}

	static class FastReader {
		BufferedReader br;
		StringTokenizer st;

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

		public FastReader(String s) throws FileNotFoundException {
			br = new BufferedReader(new FileReader(new File(s)));
		}

		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;
		}
	}

}