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:
def solve(n,k,ans):
    nums = []
    for i in range(k+1,n+1):
        nums.append(str(i))

    if k%2 == 0:
        limit = (k//2)-1
    else:
        limit = k//2
        
    for i in range(k-1,limit,-1):
        nums.append(str(i))

    ans.append(str(len(nums)))
    ans.append(' '.join(nums))

def main():
    t = int(input())
    ans = []
    for i in range(t):
        n,k = map(int,input().split())
        solve(n,k,ans)

    print('\n'.join(ans))
    

main()