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:
t = int(input())
for _ in range(t):
    n, k = map(int, input().split())
    ban = set()
    ans = []
    for i in reversed(range(1, n+1)):
        if i > k:
            ans.append(i)
        elif i == k:
            continue
        else:
            if i not in ban:
                ans.append(i)
                ban.add(k-i)
    print(len(ans))
    print(*ans)