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

public class cfpract {
   
    static class pair{
        char ch;  int fr;
        pair(char ch,int fr){this.ch=ch;  this.fr=fr;  }
    }


    public static void solve() throws Exception{
        InputStreamReader ip=new InputStreamReader(System.in);
        BufferedReader br = new BufferedReader(ip);
        int t = Integer.parseInt(br.readLine());
        StringBuilder asb=new StringBuilder();

       while(t-->0){
        // int n =Integer.parseInt(br.readLine());
        String[] strs=(br.readLine()).trim().split(" ");
        long n=Long.parseLong(strs[0]),k=Long.parseLong(strs[1]);//,r=Integer.parseInt(strs[2]),s=Integer.parseInt(strs[3]);
        //  String str=(br.readLine()).trim();
        

        if(n<k){
            asb.append("NO");  
        }else if(n==k){
            asb.append("YES");    asb.append("\n");
            for(int i=0;i<k;i++){
                asb.append(1);  asb.append(" ");
            }

        }else if(n%2==0 && n>=(2*k)){
            asb.append("YES");    asb.append("\n");

            for(int i=0;i<k-1;i++){
                n-=2;
                asb.append(2);  asb.append(" ");
            }
            asb.append(n);  asb.append(" ");
        }else if((n%2==1 && k%2==1) || (n%2==0 && k%2==0)){  //tc 6 4 ->1 1 3
            asb.append("YES");    asb.append("\n");

            for(int i=0;i<k-1;i++){
                n-=1;
                asb.append(1);  asb.append(" ");
            }
            asb.append(n);  asb.append(" ");
        }else{
            asb.append("NO");
        }

        asb.append("\n");
       }

       System.out.println(asb);
    }
   
//******************************************************************************************************************** */
    public static void main(String[] args) throws Exception{
        solve();
     }

     public static void solve2() throws Exception{
        InputStreamReader ip=new InputStreamReader(System.in);
        BufferedReader br = new BufferedReader(ip);
        int t = Integer.parseInt(br.readLine());
        StringBuilder asb=new StringBuilder();

       while(t-->0){
        // int n =Integer.parseInt(br.readLine());
        // String[] strs=(br.readLine()).trim().split(" ");
        // int n=Integer.parseInt(strs[0]),l=Integer.parseInt(strs[1]),r=Integer.parseInt(strs[2]),s=Integer.parseInt(strs[3]);
        //  String str=(br.readLine()).trim();
        
       }
    }
    //sort
     public static void sort(long[] arr) {
		int n = arr.length;
		for (int i = 0; i < n; i++) {
			int idx = (int) Math.random() * n;
			long temp = arr[i];  arr[i] = arr[idx];  arr[idx] = temp;  //swap
		}
		Arrays.sort(arr);
	}
 
	public static void sort(int[] arr) {
		int n = arr.length;
		for (int i = 0; i < n; i++) {
			int idx = (int) Math.random() * n;
			int temp = arr[i];  arr[i] = arr[idx]; arr[idx] = temp;  //swap
		}
		Arrays.sort(arr);
	}
    //1d print
    public static void print(int[] dp) {
		for (int val : dp) {
			System.out.print(val + " ");
		}
		System.out.println();
	}
 
	public static void print(long[] dp) {
		for (long val : dp) {
			System.out.print(val + " ");
		}
		System.out.println();
	}  
    //2d print
	public static void print(long[][] dp) {
		for (long[] a : dp) {
			for (long val : a) {
				System.out.print(val + " ");
			}
			System.out.println();
		}
	}
 
	public static void print(int[][] dp) {
		for (int[] a : dp) {
			for (int val : a) {
				System.out.print(val + " ");
			}
			System.out.println();
		}
	}
 
	
}