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 _ in range(int(input().strip())):
    # n = int(input().strip())
    n, k = map(int, input().strip().split())
    # a = list(map(int, input().strip().split()))
    # b = list(map(int, input().strip().split()))
    # c = list(map(int, input().strip().split()))
    # s = input().strip()

    if n == 1:
        print(0)
    else:
        x = (k+1)//2
        m = k-x
        m += n-k
        print(m)
        for i in range(x,k):
            print(i,end=' ')
        for i in range(k+1,n+1):
            print(i,end=' ')
        print()