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.*;

public class B
{
    static int count = 0;
    public static void main(String[] args)
    {
        FastReader fr = new FastReader();
        int t = fr.nextInt();
        for (int i=0; i<t; i++)
        {
            int n = fr.nextInt();
            int k = fr.nextInt();

            if (n>=k && (n-k)%2 == 0)
            {
                System.out.println("YES");
                System.out.print(n-k+1);
                while (k-- > 1)
                {
                    System.out.print(" 1");
                }
                System.out.println();
            }
            else if (n >= k*2 && n%2==0)
            {
                System.out.println("YES");
                System.out.print(n-(k*2)+2);
                while (k-- > 1)
                {
                    System.out.print(" 2");
                }
                System.out.println();
            }
            else
            {
                System.out.println("NO");
            }
        }
    }  
}

class FastReader 
{ 
    BufferedReader br; 
    StringTokenizer st; 

    public FastReader() 
    { 
        br = new BufferedReader(new InputStreamReader(System.in)); 
    } 

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

    public int nextInt() 
    { 
        return Integer.parseInt(next()); 
    } 

    long nextLong() 
    { 
        return Long.parseLong(next()); 
    } 

    double nextDouble() 
    { 
        return Double.parseDouble(next()); 
    } 

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