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:
import math
t = int(input())
j=0
while j <t:
    n,k = tuple(map(int,input().split()))
    
    if True:
        x=[]
        l=[]
        for i in range(n):
            x.append(i+1)
        for num in x[k:]:
            l.append(str(num))
        m = math.floor((k-1)/2)
        for num in x[m:k-1]:
            l.append(str(num))
        print(len(l))
        print(' '.join(l))
    j+=1