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.io.*;
import java.util.*;
import java.lang.*;
public class samepar{
    static class FastScanner {
        BufferedReader br;
        StringTokenizer st;
        FastScanner(InputStream stream) {
            try {
                br = new BufferedReader(new
                    InputStreamReader(stream));
            } catch (Exception e) {
                e.printStackTrace();
            }
        }

        String next() {
            while (st == null || !st.hasMoreTokens()) {
                try {
                    st = new StringTokenizer(br.readLine());
                } catch (IOException e) {
                    e.printStackTrace();
                }
            }
            return st.nextToken();
        }

        String nextLine() {
            String str = "";
            try
            {
                str = br.readLine();
            }
            catch (IOException e)
            {
                e.printStackTrace();
            }
            return str;
        }

        int nextInt() {
            return Integer.parseInt(next());
        }
        long nextLong() {
            return Long.parseLong(next());
        }
     }
	public static void main(String args[]) {
		try {
			FastScanner sc=new FastScanner(System.in);
			int tests=sc.nextInt();
			for(int l=0;l<tests;l++) {
			    long n=sc.nextLong();
			    int k=sc.nextInt();
			    long a[]=new long[k];
			    int x=0;
			    if(n==k) {
			    	for(int i=0;i<k;i++) {
			    		a[i]=1;
			    	}
			    }
			    else if(n>=(2*k)) {
			    	if(k%2==0 && n%2!=0) {
			    		x=-1;
			    	}
			    	else {
			    		if((((n-k)%2)&(k%2))==1) {
			    			a[0]=n-2*(k-1);
			    			for(int i=1;i<k;i++) {
			    				a[i]=2;
			    			}
			    		}
			    		else {
			    			a[0]=n-(k-1);
			    			for(int i=1;i<k;i++) {
			    				a[i]=1;
			    			}
			    		}
			    		}
			    }
			    else if(n>k && n<2*k) {
			    	if(n==(k+1))
			    		x=-1;
			    	else
			    	{
			    		if((n-k)%2==0) {
			    			a[0]=n-k+1;
			    			for(int i=1;i<k;i++) {
			    				a[i]=1;
			    			}
			    		}
			    		else x=-1;
			    	}
			    }
			    else {
			    	x=-1;
			    	}
			    if(x==-1) {
			    	System.out.println("NO");
			    }
			    else {
			    	System.out.println("YES");
			    	for(int i=0;i<k;i++) {
			    		System.out.print(a[i]+" ");
			    	}
			    	System.out.println();
			    }
			}
		}
		catch(Exception e) {}
	
}
}