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):
    nums = set(range(1, n+1))

    nums.discard(k)
    for i in range(k):
        if k - i != i and k - i in nums:
            nums.discard(i)
    return nums


def verify(nums, k):
    snums = sorted(nums)
    for i in reversed(range(len(nums))):
        if snums[i] <= k:
            k -= snums[i]

    return k != 0


if __name__ == "__main__":
    for _ in range(int(input())):
        n, k = map(int, input().split(" "))
        res = solve(n, k)
        if verify(res, k):
            print(len(res))
            print(" ".join(map(str, res)))
        else:
            raise Exception