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 p2 {
    public static class Pair{
        Pair(){
        }
    }
    public static int solve(){
        return 0;
    }
    public static void main(String[] args) {
        Scanner s=new Scanner(System.in);
        int t=s.nextInt();
        StringBuilder str=new StringBuilder();
        while(t-->0){
             int num=s.nextInt();
             int k=s.nextInt();
             if(num%2!=0 && k%2==0){
                 str.append("No").append("\n");
             }
             else if(num==k){
                 str.append("Yes").append("\n");
                 for(int i=0;i<k;i++){
                     str.append(1).append(" ");
                 }
                 str.append("\n");
             }
            else {
                int n1=num-2*(k-1);
                int n2=num-(k-1);
                if(n1%2==0 && n1>0){
                    str.append("YES").append("\n");
                    str.append(n1).append(" ");
                    for(int i=0;i<k-1;i++){
                        str.append(2).append(" ");
                    }
                    str.append("\n");
                }
                else if(n2%2==1 && n2>0){
                    str.append("YES").append("\n");
                    str.append(n2).append(" ");
                    for(int i=0;i<k-1;i++){
                        str.append(1).append(" ");
                    }
                    str.append("\n");
                }
                else{
                    str.append("No").append("\n");
                }
             }
        }
        System.out.println(str);
    }

}