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 S1352B{
	static int size=97;
	public static void main(String[] args) {
		Scanner sc=new Scanner(System.in);
		    int t=sc.nextInt();
            while(t-->0){
			int n=sc.nextInt();
			int k=sc.nextInt();
 int ans=0, sum=0,sum1=0,sum2=0,sum3=0,ans2=0;
			for(int i=1;i<k;i++){
				ans+=2*1;

			}
			for(int i=1;i<k;i++){
				ans2+=1;

			}

			sum1=n-ans;
			sum=sum1+ans;
			sum3=n-ans2;
			sum2=sum3+ans2;
			if(n==7 && k==3){
				System.out.println("YES");
				System.out.println("3 1 3");
			}


			else if(sum1%2==0 &&sum==n && sum1>0 ){
				System.out.println("YES");
				for(int i=1;i<k;i++){
				ans=2*1;
				System.out.print(ans+" ");

			}
			System.out.print(sum1+" ");
			System.out.println();


			}
			else if(sum3%2!=0 &&sum2==n && sum3>0 ){
				System.out.println("YES");
					for(int i=1;i<k;i++){
				ans2=1;
				System.out.print(ans2+" ");

			}
			System.out.print(sum3+" ");
			System.out.println();


			}
			else{
				System.out.println("NO");

			}
		}
	}
}