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

public class HelloWorld{

     public static void main(String []args) throws IOException{
        BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
        int t= Integer.parseInt(br.readLine());
        while(t-->0)
        {
            String []s = br.readLine().split(" ");
            int n=Integer.parseInt(s[0]);
            int k=Integer.parseInt(s[1]);
            int check = n - (k-1);
            StringBuilder sb = new StringBuilder();
            
            if(check>0 && check % 2 != 0)
            {
                System.out.println("YES");
                for(int i=0;i<k-1;i++)
                    sb.append("1 ");
                sb.append(check);
                
                System.out.println(sb);
                continue;
            } else if(n%2 == 0)
            {
                check = n - (k-1) * 2;
                if(check>0 && check % 2 == 0)
                {
                    System.out.println("YES");
                    for(int i=0;i<k-1;i++)
                        sb.append("2 ");
                    sb.append(check);
                System.out.println(sb);
                    continue;
                }
            }
            System.out.println("NO");
        }
     }
}