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
def solve(n,k):
    # arr=[1 for _ in range(k)]
    # for i in reversed(range(len(arr))):
    #     arr[len(arr)-i]
    # a=k//2
    ans=[i for i in range(math.ceil(k/2),k)]+[a for a in range(k+1,n+1)]
    print(len(ans))
    string=" ".join(map(str,ans))
    print(string)


x=int(input())
for _ in range(x):
    A = list(map(int, input().split()))
    solve(A[0],A[1])