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
{
	public static void main (String[] args) throws java.lang.Exception
	{
		// your code goes here
		Scanner sc = new Scanner(System.in);
		int test = sc.nextInt();
		while(test-->0){
		    int num = sc.nextInt();
		    int k = sc.nextInt();
		    int rem = num-(k-1);
		    if(rem%2==1 && rem>0){
		        System.out.println("yes");
		        for(int i=0;i<k-1;i++){
		            System.out.print(1+" ");
		        }
		        System.out.println(rem);
		    }else{
		        rem = num-2*(k-1);
		    if(rem%2==0 && rem>0){
		        System.out.println("yes");
		        for(int i=0;i<k-1;i++){
		            System.out.print(2+" ");
		        }
		        System.out.println(rem);
		    }else{
		        System.out.println("no");
		    }
		    }
		}
	}
}