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.lang.*;
import java.util.*;
import java.io.*;
public class MyClass{
    
    public static boolean check_even(int n,int k){
        int rem = n-2*k;
        if(rem<0){
            return false;
        }
        if(rem%2==1){
            return false;
        }
        System.out.println("YES");
        for(int i=0;i<k-1;i++){
            System.out.print("2"+" ");
        }
        System.out.print(2+rem);
        
        System.out.println("");
        return true;
    }
    
    public static boolean check_odd(int n,int k){
        int rem = n-k;
        if(rem<0){
            return false;
        }
        if(rem%2==1){
            return false;
        }
        System.out.println("YES");
        for(int i=0;i<k-1;i++){
            System.out.print("1"+" ");
        }
        System.out.print(1+rem);
        
        System.out.println("");
        return true;
    }
    
    public static void main(String[] args){
        Scanner scan = new Scanner(System.in);
        int t= scan.nextInt();
        while(t-->0){
           int n = scan.nextInt();
           int k = scan.nextInt();
           if(check_even(n,k) || check_odd(n,k)){
               continue;
           }
           else{
               System.out.println("NO");
           }
        }
    }
}