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.lang.*;
import java.io.*;
import java.math.*;
//BigInteger A;
//A= BigInteger.valueOf(54);
//ArrayList<Integer> a=new ArrayList<>();
//TreeSet<Integer> ts=new TreeSet<>();
//HashMap<Integer,Integer> hm=new HashMap<>();
//PriorityQueue<Integer> pq=new PriorityQueue<>();
public final class CF
{
	public static void main(String[]args)throws IOException
	{
		//int K=(int)Math.pow(10,9)+7;
          FastReader ob=new FastReader();
          StringBuffer sb=new StringBuffer();
          int t=ob.nextInt();
          while(t-->0)
          {
               int n=ob.nextInt();
               int k=ob.nextInt();
               if(k>n)
               sb.append("NO");
               else if(k==n)
               {
                   sb.append("YES\n");
                    for (int i = 0; i < k; i++) {
                        sb.append(1+" ");
                    }
               }
               else
               {
                   int x=n-(k-1)*2;
                   if(x>0&&x%2==0)
                   {
                       sb.append("YES\n");
                        for (int i = 0; i < k-1; i++) {
                               sb.append(2+" ");
                           }
                           sb.append(x);
                   }
                   else
                   {
                       x=n-(k-1);
                       if(x>0&&x%2!=0)
                       {
                           sb.append("YES\n");
                           for (int i = 0; i < k-1; i++) {
                               sb.append(1+" ");
                           }
                           sb.append(x);
                       }
                       else
                       sb.append("NO");
                   }
               }
               sb.append("\n");
          }
          System.out.println(sb);
	}
}
class Pair
{
	int x,y;
	Pair(int x,int y)
	{
		this.x=x;
		this.y=y;
	}
}
class PairComparator implements Comparator<Pair>
{
	public int compare(Pair a,Pair b)
	{
		return a.x-b.x;
	}
}
class FastReader {
    BufferedReader br;
    StringTokenizer st;
    public FastReader() {
        br = new BufferedReader(new InputStreamReader(System.in));
    }

    public String next() {
        while (st == null || !st.hasMoreElements()) {
            try {
                st = new StringTokenizer(br.readLine());
            } catch (IOException e)  {
                e.printStackTrace();
            }
        }
        return st.nextToken();
    }
    public String nextLine()
    {
        String s="";
        try {
        s=br.readLine();
        } catch (IOException e)  {
                e.printStackTrace();
            }
        return s;
    }
    public int nextInt() {
        return Integer.parseInt(next());
    }
    public long nextLong() {
        return Long.parseLong(next());
    }
    public double nextDouble() {
        return Double.parseDouble(next());
    }
}