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 PYTHON):

Solution:

for _ in range(input()):
    n,k=map(int,raw_input().split())
    l=[]
    if k%2==0:
        mid=k/2
    else:
        mid=(k+1)/2
    while mid<=n:
        if mid!=k:
            l.append(mid)
        mid+=1
    if len(l)==0:
        print 0
    else:
        print len(l)
        for i in l:
            print i,
        print