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
import math
cases = int(input())
for case in range(0, cases):
    inputs = [int(x) for x in input().split(" ")]
    n = inputs[0]
    k = inputs[1]
    m = n - k + math.ceil((k-1)/2)
    array = list(range(n,k,-1)) + list(range(k-1,math.ceil((k-1)/2)-1,-1))
    
    print(m)
    print(array)