Problem: You are given two positive integers n (1 ≤ n ≤ 10^9) and k (1 ≤ k ≤ 100). Represent the number n as the sum of k positive integers of the same parity (have the same remainder when divided by 2).

In other words, find a_1, a_2, …, a_k such that all a_i>0, n = a_1 + a_2 + … + a_k and either all a_i are even or all a_i are odd at the same time.

If such a representation does not exist, then report it.

Input

The first line contains an integer t (1 ≤ t ≤ 1000) — the number of test cases in the input. Next, t test cases are given, one per line.

Each test case is two positive integers n (1 ≤ n ≤ 10^9) and k (1 ≤ k ≤ 100).

Output

For each test case print:

  * YES and the required values a_i, if the answer exists (if there are several answers, print any of them); 
  * NO if the answer does not exist. 



The letters in the words YES and NO can be printed in any case.

Example

Input


8
10 3
100 4
8 7
97 2
8 8
3 10
5 3
1000000000 9


Output


YES
4 2 4
YES
55 5 5 35
NO
NO
YES
1 1 1 1 1 1 1 1
NO
YES
3 1 1
YES
111111110 111111110 111111110 111111110 111111110 111111110 111111110 111111110 111111120

Solution (in JAVA):

Solution:
import java.util.*;
import java.io.*;
public class A  {
    static FastReader in=new FastReader();
    static final Random random=new Random();
    static long mod=1000000007L;

    public static void main(String args[]) throws IOException {
        int t=in.nextInt();
        StringBuilder res=new StringBuilder();
        
        loop:
        while(t-->0)
        {
        	
        	int n=in.nextInt();
        	int k=in.nextInt();
        	if(n%2==0&&k%2==0)
        	{
        		if(n<k)
        		{
        			res.append("No\n");
        			
        		}
        		else 
        		{
        			res.append("Yes\n");
        			for(int i=1;i<k;i++)
        			{
        				res.append("1 ");
        			}
        			res.append(n-(k-1)+"\n");
        		}
        		continue loop;
        	}
        	if(n%2!=0&&k%2!=0)
        	{
        		if(n<k)
        		{
        			res.append("No\n");
        			
        		}
        		else 
        		{
        			res.append("Yes\n");
        			for(int i=1;i<k;i++)
        			{
        				res.append("1 ");
        			}
        			res.append(n-(k-1)+"\n");
        		}
        		continue loop;
        	}
        	if(n%2==0&&k%2!=0)
        	{
        		if(n<2*k)
        		{
        			res.append("No\n");
        			
        		}
        		else 
        		{
        			res.append("Yes\n");
        			for(int i=1;i<k;i++)
        			{
        				res.append("2 ");
        			}
        			res.append(n-2*(k-1)+"\n");
        		}
        		continue loop;
        	}
        	if(n%2!=0&&k%2==0)
        	{
        		res.append("No\n");
        		continue loop;
        	}
        	
        	
        	
        }
        print(res);
    }
    
    

    static long power(long x, long y, long p) 
    { 

        long res = 1;      
         
 
        x = x % p;  
  
       if (x == 0) return 0;   
  
        while (y > 0) 
        { 
         
            if((y & 1)==1) 
                res = (res * x) % p; 
      
            y = y >> 1;  
            x = (x * x) % p;  
        } 
        return res; 
    } 
     
    static void ruffleSort(int[] a) {
        int n=a.length;
        for (int i=0; i<n; i++) {
            int oi=random.nextInt(n), temp=a[oi];
            a[oi]=a[i]; a[i]=temp;
        }
        Arrays.sort(a);
    }

    static < E > void print(E res)
    {
        System.out.println(res);
    }


    static  int gcd(int a,int b)
    {
        if(b==0)
        {
            return a;
        }
        return gcd(b,a%b);
    }
    
    static int lcm(int a, int b)
    {
        return (a / gcd(a, b)) * b;
    }

    
    static int abs(int a)
    {
        if(a<0)
            return -1*a;
        return 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;
        }

        int [] readintarray(int n) {
            int res [] = new int [n];
            for(int i = 0; i<n; i++)res[i] = nextInt();
            return res;
        }
        long [] readlongarray(int n) {
            long res [] = new long [n];
            for(int i = 0; i<n; i++)res[i] = nextLong();
            return res;
        }
    }

}