You are given two integers n and k. You are asked to choose maximum number of distinct integers from 1 to n so that there is no subset of chosen numbers with sum equal to k.

A subset of a set is a set that can be obtained from initial one by removing some (possibly all or none) elements of it.

Input

The first line contains the number of test cases T (1 ≤ T ≤ 100).

Each of the next T lines contains two integers n and k (1 ≤ k ≤ n ≤ 1000) — the description of test cases.

Output

For each test case output two lines. In the first line output a single integer m — the number of chosen integers.

In the second line output m distinct integers from 1 to n — the chosen numbers.

If there are multiple answers, print any. You can print the numbers in any order.

Example

Input


3
3 2
5 3
1 1


Output


2
3 1 
3
4 5 2 
0
from collections import defaultdict,deque,Counter
import sys
import bisect
import math
input=sys.stdin.readline
mod=1000000007
    
n=int(input())
for ii in range(n):
        n,k=map(int,input().split())
        ans=[int(i) for i in range(k+1,n+1)]
        for i in range(1,k//2+1):
                ans.append(i)
        print(len(ans))
        print(*ans)
       
            


    
    
        
    

        

           
                


    
    

           
                


    
    
       
            


    
    
        
    

        

           
                


    
    

           
                


    
    
       
            


    
    
        
    
           
                


    
    
       
            


    
    
        
    
            

    
    

           
                


    
    
       
            


    
    
        
    

        

           
                


    
    

           
                


    
    
       
            


    
    
        
    

        

           
                


    
    

           
                


    
    
       
            


    
    
        
    


           
                


    
    

           
                


    
    
       
            


    
    
        
    

        

           
              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