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 src;

import java.util.Scanner;
import java.util.HashMap;
import java.util.HashSet;
import java.util.Iterator;
import java.util.PriorityQueue;
import java.util.Queue;
import java.util.Stack;
import java.util.StringTokenizer;
import java.util.TreeMap;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.Collections;
import java.io.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.lang.StringBuilder;
import java.math.BigInteger;

public class idk {
	static Scanner scn = new Scanner(System.in);

	public static void main(String[] args) {
		
			int t=scn.nextInt();
			while(t-->0)
			{
				long n=scn.nextLong();
				int k=scn.nextInt();
				if(n%k==0)
				{
					System.out.println("YES");
					for(int i=0;i<k;i++)
						System.out.print(n/k+" ");
					System.out.println();
				}
				else if(k>n||(n%2!=0&&k%2==0))
					System.out.println("NO");
				else if(n%2==0&&k%2==0)
				{
					if(k<=n/2)
					{
						System.out.println("YES");
						for(int i=0;i<k;i++)
						{
							if(i!=k-1)
								System.out.print("2"+" ");
							else
								System.out.println(n-2*i);
						}
					}
					else if(k>n/2)
					{
						System.out.println("YES");
						for(int i=0;i<k;i++)
						{
							if(i!=k-1)
								System.out.print("1"+" ");
							else
								System.out.println(n-i);
						}
						
					}
				}
				else if(n%2==0&&k%2!=0)
				{
					if(2*k<=n)
					{
						System.out.println("YES");
						for(int i=0;i<k;i++)
						{	if(i!=k-1)
							System.out.print("2"+" ");
						else
							System.out.println(n-2*(i));
						}
						
					}
					else System.out.println("NO");
				}
				else if(n%2!=0&&k%2!=0)
				{
					if(k<=n)
					{
						System.out.println("YES");
						for(int i=0;i<k;i++)
						{
							if(i!=k-1)
								System.out.print("1 ");
							else
							{
								System.out.println(n-i);
							}
						}
					}
					else
						System.out.println("NO");
				}
				
						
			}
		
	}

	public static long gcd(long a, long b) {
		if (a == 0)
			return b;
		return gcd(b % a, a);
	}

	public static String factorial(int n) {
		BigInteger fac = new BigInteger("1");
		for (int i = 1; i <= n; i++) {
			fac = fac.multiply(BigInteger.valueOf(i));
		}
		return fac.toString();
	}

}