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:
//BUNCH OF IMPORTS
import java.util.Scanner;
import java.util.Random;
import java.util.Collections;
import java.util.Arrays;
import java.util.ArrayList;
import java.util.StringTokenizer; 
import java.io.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;

//MAIN CLASS
public class practice
{
	static FastReader input = new FastReader();
	static void test_case()
	{
		Long n = input.nextLong();
		int k = input.nextInt();
		Long case1 = n-k+1;
		Long case2 = n-(2*(k-1));

		Boolean yes = false;
		if((case1%2!=0 && case1 > 0))
		{
			yes= true;
			System.out.println("YES");
			for(int i=0;i<k-1;i++)
			{
				System.out.print("1 ");
			}
			System.out.print(case1+"\n");
		}
		else if((case2%2==0 && case2 > 0) && yes == false)
		{
			System.out.println("YES");
			for(int j=0;j<k-1;j++)
			{
				System.out.print("2 ");
			}
			System.out.print(case2+"\n");

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


	}
	public static void main(String[]args)
	{
		practice call = new practice();
		int number_of_test_cases = input.nextInt();
		for(int i=0;i<number_of_test_cases;i++)
		{		
			call.test_case();
		}
	}
}




//FAST READER CLASS FOR FASTER INPUT AND OUTPUT
class FastReader
{
	private BufferedReader br;
	private StringTokenizer st;
	public FastReader()
	{
		br = new BufferedReader(new InputStreamReader(System.in));
		//BufferReader creates an input stream which enables reading data
		//Then, InputStreamReader reads the stream through System.in

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

	int nextInt()
	{
		return Integer.parseInt(inputter());
	}
	Long nextLong()
	{
		return Long.parseLong(inputter());	
	}
	Double nextDouble()
	{
		return Double.parseDouble(inputter());	
	}
	String next()
	{
		return inputter();		
	}
	String nextLine()
	{
		String theString = " ";
		try
		{
			theString = br.readLine();
		}
		catch(IOException e)
		{
			e.printStackTrace();
		}
		return theString;	
	}
}