Problem: 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

Solution (in PYTHON3):

Solution:
import math
import sys
from collections import *
 
 
def cint() : return list(map(int, sys.stdin.readline().strip().split()))
def cstr() : return list(map(str, input().split(' '))) 



 
def solve(t):
    n,k = cint()

    lst = []
    for i in range(k+1,n+1):
        lst.append(i)

    s = set()
    for i in range(k-1,0,-1):
        if i not in s:
            lst.append(i)
            s.add(k-i)

    print(len(lst))
    for item in lst: print(item,end=' ')
    print()

    
    

    
 
if __name__ == "__main__":
    t = int(input())
    # t =1
    
    for i in range(1,t+1):
        solve(i)