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:
for i in range(int(input())):
#for i in range(1):
    n, k = map(int, input().split())
   # n,k=3,2
    res = []
    if n!=1:


        for i in range(n, k, -1):
            if i!=0:
                res.append(i)

        if k % 2 == 0:
            for i in range(k//2,k):
                if i!=0:
                    res.append(i)

        else:
            #print((k - 1) // 2,(k - 1) // 2-1)
            for i in range((k//2)+1,k):
                if i!=0:
                    res.append(i)

    print(len(res))
    if len(res)!=0:
        print(" ".join(map(str, res)))