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 A {
    static 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(); 
        } 
  
        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; 
        } 
    } 
    static int gcd(int a, int b) 
    { 
    if (a == 0) 
        return b;  
    return gcd(b % a, a);  
    } 
      
    
    static int lcm(int a, int b) 
    { 
        return (a*b)/gcd(a, b); 
    } 
    

    public static void main(String[] args) {
        FastReader s = new FastReader();
        int t = s.nextInt();
        while(t-- >0){
           
            long n = s.nextLong();
            long k = s.nextLong();
            boolean ans1 =false;
            boolean ans2 =false;
            
            if((n-k+1)%2==1 && (n-k+1)>0 ){
                ans1 = true;
                System.out.println("YES");
                long num = n-k+1;
                System.out.print(num + " ");
                for(long i=0;i<k-1;i++){
                    System.out.println(1 + " ");
                }
                System.out.println("");
                continue;
            }
            if((n-2*(k-1))%2==0 && (n-2*(k-1))>0){
                ans2 = true;
                
                System.out.println("YES");
                
                long num = n - 2*(k-1);
                System.out.print(num + " ");
                for(long i=0;i<k-1;i++){
                    System.out.println(2 + " ");
                }
                System.out.println("");
                continue;
            } 
            
            if(!ans1 && !ans2){
                System.out.println("NO");
            }
            
            
            
            

            
           
            
            
                
            
        }   
    }
}