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.io.BufferedReader;
import java.io.IOException;
import java.io.InputStream;
import java.io.InputStreamReader;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.HashSet;
import java.util.Hashtable;
import java.util.StringTokenizer;

public class Solution {
	public static void main ( String args [] ) throws IOException, InterruptedException {
	
	
			solve();}


public static void solve() throws IOException, InterruptedException {
Scanner sc = new Scanner(System.in);
int x= sc.nextInt();
all:for(int i=0;i<x;i++) {
	StringBuilder sb = new StringBuilder("");
int n=sc.nextInt();
int k=sc.nextInt();
if((n-(k-1))% 2 ==1 && (n-(k-1))>0) {
	System.out.println("YES");

for(int j=0;j<k-1;j++) {
	sb.append("1 ");
}
sb.append(n-(k-1));
System.out.println(sb);
continue all;}
if((n-(2*(k-1)))%2==0 && (n-(2*(k-1)))>0) {
	System.out.println("YES");
	for(int j=0;j<k-1;j++) {
		sb.append("2 ");
	}
	sb.append(n-(2*(k-1)));
	System.out.println(sb);
	continue all;}
System.out.println("NO");
}

}









	
	
	
	
	
	



















static void shuffle(int[] a)
{
	int n = a.length;
	for(int i = 0; i < n; i++)
	{
		int r = i + (int)(Math.random() * (n - i));
		int tmp = a[i];
		a[i] = a[r];
		a[r] = tmp;
	}
}




}

@SuppressWarnings("rawtypes")
class Pair implements Comparable{
	int x;
	int y;

	@Override
	public int hashCode() {
		final int prime = 31;
		int result = 1;
		result = prime * result + x;
		result = prime * result + y;
		return result;
	}

	@Override
	public boolean equals(Object obj) {
		if (this == obj)
			return true;
		if (obj == null)
			return false;
		if (getClass() != obj.getClass())
			return false;
		Pair other = (Pair) obj;
		if (x != other.x)
			return false;
		if (y != other.y)
			return false;
		return true;
	}

	public Pair(int x , int y) {
		this.x=x;
		this.y=y;
	}

	@Override
	public int compareTo(Object o) {
		Pair p = (Pair)o;
		if(this.x<p.x) return -1;
		if(this.y>p.y) return 1;
		return 0;
	}


}




class Scanner 
{
	StringTokenizer st;
	BufferedReader br;

	public Scanner(InputStream s){	br = new BufferedReader(new InputStreamReader(s));}

	public String next() throws IOException 
	{
		while (st == null || !st.hasMoreTokens()) 
			st = new StringTokenizer(br.readLine());
		return st.nextToken();
	}

	public int nextInt() throws IOException {return Integer.parseInt(next());}
	
	public long nextLong() throws IOException {return Long.parseLong(next());}

	public String nextLine() throws IOException {return br.readLine();}
	
	public double nextDouble() throws IOException
	{
		String x = next();
		StringBuilder sb = new StringBuilder("0");
		double res = 0, f = 1;
		boolean dec = false, neg = false;
		int start = 0;
		if(x.charAt(0) == '-')
		{
			neg = true;
			start++;
		}
		for(int i = start; i < x.length(); i++)
			if(x.charAt(i) == '.')
			{
				res = Long.parseLong(sb.toString());
				sb = new StringBuilder("0");
				dec = true;
			}
			else
			{
				sb.append(x.charAt(i));
				if(dec)
					f *= 10;
			}
		res += Long.parseLong(sb.toString()) / f;
		return res * (neg?-1:1);
	}
	
	public boolean ready() throws IOException {return br.ready();}


}