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:
/* package codechef; // don't place package name! */

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

/* Name of the class has to be "Main" only if the class is public. */
public class Main
{
	 //[1000000];
	
	public static void main (String[] args) throws java.lang.Exception
	{
		// your code goes here
		BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
		int t = Integer.parseInt(br.readLine());
		
		
		
		while(t--!=0){
		    ArrayList<Long> dp  =new ArrayList<Long>();
		    String[] in = br.readLine().split(" ");
		    
		    long n = Long.parseLong(in[0]);
		    long k = Long.parseLong(in[1]);
		    if(n%2==1 && k%2==0){
		        System.out.println("NO");
		        continue;
		    }
		    boolean flag = true;
		    
		    long rem = n;
		    if((n%2==0 && k%2==0) || (n%2==1 && k%2==1)){
		        for(int i=0;i<k-1;i++){
		            dp.add((long)1);
		            
		            rem-=1;
		            if(rem<=0){
		                flag = false;
		                break;
		            }
		        }
		        dp.add(rem);
		    }
		    else if((n%2==0 && k%2==1)){
		        for(int i=0;i<k-1;i++){
		            dp.add((long)2);
		            
		            rem-=2;
		            if(rem<=1){
		                flag = false;
		                break;
		            }
		        }
		        dp.add(rem);
		    }
		    if(!flag){
		        System.out.println("NO");
		        continue;
		    }else{
		        System.out.println("YES");
		        for(int i=0;i<dp.size();i++){
		            System.out.print(dp.get(i)+" ");
		        }
		        System.out.println();
		    }
	}
}}