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.Arrays;
import java.util.Comparator;
import java.util.Scanner;

public class hef {
	

	
    public static void main(String[] args) {
		
    	Scanner s = new Scanner(System.in);
    	int t = s.nextInt();
    	
    	while(t--!=0) {
    		int n = s.nextInt();
        	int k = s.nextInt();
        	
        	if(k==1) {
        		System.out.println("YES");
        		System.out.println(n);
        		continue;
        	}
        	int ans = n/k;
        	int a1[] = new int[k];
        	for(int i=0;i<k;i++) {
        		a1[i] = ans;
        	}
        	if(n%k!=0) {
        		a1[k-1]+=n%k;
        	}
        	if((a1[k-1]%2!=0 && a1[k-2]%2==0) || (a1[k-1]%2==0 && a1[k-2]%2!=0)) {
        		for(int i=0;i<k-1;i+=2) {
        			a1[i]++;
        			if(i+1<k-1)
        			a1[i+1]--;
        		}
        	}
        	
        	int flag=0,sum=0;
        	for(int i=0;i<k;i++) {
        		if(a1[i]<=0) {
        			flag=1;
        			break;
        		}
        		sum+=a1[i];
        	}
        	if(flag==1 || sum!=n) {
        		System.out.println("NO");
        	}
        	else {
        		System.out.println("YES");
        		for(int i:a1) {
        			System.out.print(i+" ");
        		}
        		System.out.println();
        	}
    	}
    	
    	
	}
}