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:
from functools import lru_cache
from itertools import combinations

if __name__ == '__main__':
    for _ in range(int(input())):
        n, k = list(map(int, input().split()))

        post_k = tuple(range(k + 1, n + 1))
        pre_k = tuple(range((k + 1) // 2, k))

        ans = pre_k + post_k
        print(len(ans))
        if ans:
            print(' '.join(map(str, ans)))