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 hg in range(t) :
    n , k = map(int , input().split())
    
    l = []
    for i in range(k + 1 , n + 1):
        l.append(i)
        
    for i in reversed(range(1 , k)):
        d = k - i
        if d not in l:
            l.append(i)
    
    print(len(l))
    for i in l:
        print(int(i) , end = " ")
    print()