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.*;
public class Solution
{
    public static void main(String args[])
    {
        Scanner s= new Scanner(System.in);
        int t=s.nextInt();

        while(t>0)
        {
            int n=s.nextInt();
            int k=s.nextInt();

            if(n<k)
            {
                System.out.println("NO");
                t--;
                continue;
            }
            ArrayList<Integer> ans=new ArrayList<Integer>();
            int x=0;
            int temp;
            int temp1;
            if(n%k==0)
            {
                temp=n/k;
                for(int i=0;i<k;i++)
                    ans.add(temp);
            }
            else 
            {
                temp=n/k;
                temp1=n%k;
                if(temp1%2==0)
                {
                    ans.add(temp+temp1);
                    for(int i=0;i<k-1;i++)
                        ans.add(temp);
                }
                else
                {
                    if(k%2==0)
                        x=1;
                    else
                    {
                        if(temp==1)
                            x=1;
                        else
                        {
                            ans.add(temp+temp1);
                            int flag=1;
                            for(int i=0;i<k-1;i++)
                            {
                                ans.add(temp+flag);
                                flag=-flag;
                            }
                        }
                        
                    }
                }
            }

            if(x==1)
                System.out.println("NO");
            else
            {
                System.out.println("YES");
                for(int i=0;i<ans.size();i++)
                    System.out.print(ans.get(i)+" ");
            }
            
            System.out.println();
            t--;
        }
    
     }  
    
}