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.InputStreamReader;
import java.util.*;


public class A {

	public static void main(String[] args) {
		FastScanner fs = new FastScanner();
	     int t=fs.nextInt();
	     while(t-->0) {
	    	 int n= fs.nextInt();
	    	 int k=fs.nextInt();
	    	int n1 = n-(k-1);
	    	if(n1>0&&n1%2!=0) {
	    		System.out.println("YES");
	    		for(int i=0;i<k-1;i++) System.out.print(1+" ");
	    	    System.out.println(n1); 
	    	   continue;
	    	}
	    	int n2 =n-2*(k-1);
	    	if(n2>0&&n2%2==0) {
	    		System.out.println("YES");
	    		for(int i=0;i<k-1;i++) System.out.print(2+" ");
	    	    System.out.println(n2); 
	    	   continue;
	    	}
	    	else System.out.println("NO");
	    	
	     }
	    	
	     
	    	 }

	static void sort(int[] a ) {
		ArrayList<Integer> l = new ArrayList<>();
		for(int i:a) l.add(i);
		Collections.sort(l);
		for(int i=0;i<l.size();i++) a[i]=l.get(i);
	}
	static class FastScanner {
		BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
		StringTokenizer st = new StringTokenizer("");
		String next() {
			while(!st.hasMoreTokens())
				try {
					st = new StringTokenizer(br.readLine());
				}catch(IOException e) {
					e.printStackTrace();
				}
			return st.nextToken();
		}
		int nextInt() {
			return Integer.parseInt(next());
		}
		int[] readArray(int n) {
			int[] a = new int[n];
			for(int i=0;i<n;i++)a[i]=nextInt();
			return a;
		}
		long nextLong() {
			return Long.parseLong(next());
		}
	}

}