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 TestClass {
    public static void main(String args[] ) throws Exception {

        BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
        BufferedWriter bw = new BufferedWriter(new OutputStreamWriter(System.out));
     
        int t=Integer.parseInt(br.readLine());
        while(t-->0)
        {
            String str[]=br.readLine().split(" ");
            int n=Integer.parseInt(str[0]);
            int k=Integer.parseInt(str[1]);
            boolean flag=true;
                    ArrayList<Integer> al=new ArrayList<>();
                    int p=1;
                    int sum=0;
                    for(int i=1;i<k;i++)
                    {
                        sum=sum+p;
                        al.add(p);
                       
                    }
                    if(sum<n&&(n-sum)%2==1)
                    {
                        al.add(n-sum);
                        bw.write("YES\n");
                        for(int i=0;i<al.size();i++)
                        bw.write(al.get(i)+" ");
                        bw.newLine();
                        flag=false;
                    }
                    if(flag)
                    {
                        al.clear();
                     p=2;
                    sum=0;
                    for(int i=1;i<k;i++)
                    {
                        sum=sum+p;
                        al.add(p);
                       
                    }
                    if(sum<n&&(n-sum)%2==0)
                    {
                        al.add(n-sum);
                        bw.write("YES\n");
                        for(int i=0;i<al.size();i++)
                        bw.write(al.get(i)+" ");
                        bw.newLine();
                       
                    }
                    else
                    bw.write("NO\n");
                    
                        
                    }
                    
        }
                  bw.close();  
        }

}