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
import java.util.*;import java.io.*;import java.math.*;
public class Main
{
    static class Node{
        int x;
        int y;
        Node(int x,int y){
            this.x=x;
            this.y=y;
        }
    }
    public static void process()throws IOException
    {
        long a=nl();
        long b=nl();
        ArrayList<Node>l1=new ArrayList<Node>();
        ArrayList<Node>l2=new ArrayList<Node>();
        a=a*a;
        b=b*b;
        for(int i=1;i<=a/2;i++)
            if(isPerfect(i) && isPerfect(a-i))
                l1.add(new Node((int)Math.sqrt(i),(int)Math.sqrt(a-i)));
        for(int i=1;i<=b/2;i++)
            if(isPerfect(i) && isPerfect(b-i))
                l2.add(new Node((int)Math.sqrt(i),(int)Math.sqrt(b-i)));
        for(Node one:l1)
        {
            for(Node two:l2)
            {
                if((one.x*two.x)-(one.y*two.y)==0)
                {
                    pn("YES");
                    pn("0 0");
                    pn(one.x+" "+one.y);
                    if(two.y==one.y)
                        pn((two.x)+" "+(-two.y));
                    else
                        pn((-two.x)+" "+two.y);
                    return;
                }
                if((one.x*two.y)-(one.y*two.x)==0)
                {
                    pn("YES");
                    pn("0 0");
                    pn(one.x+" "+one.y);
                    if(two.x==one.y)
                        pn((two.y)+" "+(-two.x));
                    else
                        pn((-two.y)+" "+two.x);
                    return;
                }
            }
        }
        pn("NO");
    }
    static boolean isPerfect(long x)
    {
        long temp=(long)Math.sqrt(x);
        if(temp*temp==x)
            return true;
        return false;
    }

    static AnotherReader sc;
    static PrintWriter out;
    public static void main(String[]args)throws IOException
    {
        boolean oj = System.getProperty("ONLINE_JUDGE") != null;
        if(oj){sc=new AnotherReader();out=new PrintWriter(System.out);}
        else{sc=new AnotherReader(100);out=new PrintWriter("output.txt");}
        int t=1;
        // t=ni();
        while(t-->0) {process();}
        out.flush();out.close();  
    }

    static void pn(Object o){out.println(o);}
    static void p(Object o){out.print(o);}
    static void pni(Object o){out.println(o);out.flush();}
    static int ni()throws IOException{return sc.nextInt();}
    static long nl()throws IOException{return sc.nextLong();}
    static double nd()throws IOException{return sc.nextDouble();}
    static String nln()throws IOException{return sc.nextLine();}
    static int[] nai(int N)throws IOException{int[]A=new int[N];for(int i=0;i!=N;i++){A[i]=ni();}return A;}
    static long[] nal(int N)throws IOException{long[]A=new long[N];for(int i=0;i!=N;i++){A[i]=nl();}return A;}
    static long gcd(long a, long b)throws IOException{return (b==0)?a:gcd(b,a%b);}
    static int gcd(int a, int b)throws IOException{return (b==0)?a:gcd(b,a%b);}
    static int bit(long n)throws IOException{return (n==0)?0:(1+bit(n&(n-1)));}

/////////////////////////////////////////////////////////////////////////////////////////////////////////

    static class AnotherReader{BufferedReader br; StringTokenizer st;
    AnotherReader()throws FileNotFoundException{
    br=new BufferedReader(new InputStreamReader(System.in));}
    AnotherReader(int a)throws FileNotFoundException{
    br = new BufferedReader(new FileReader("input.txt"));}
    String next()throws IOException{
    while (st == null || !st.hasMoreElements()) {try{
    st = new StringTokenizer(br.readLine());}
    catch (IOException  e){ e.printStackTrace(); }}
    return st.nextToken(); } int nextInt() throws IOException{
    return Integer.parseInt(next());}
    long nextLong() throws IOException
    {return Long.parseLong(next());}
    double nextDouble()throws IOException { return Double.parseDouble(next()); }
    String nextLine() throws IOException{ String str = ""; try{
    str = br.readLine();} catch (IOException e){
    e.printStackTrace();} return str;}}
   
/////////////////////////////////////////////////////////////////////////////////////////////////////////////
}