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

m = int(input())
for i in range(0,m):
    n,k = map(int, input().split(" "))
    answer = math.floor(n/2) + 1
    if answer == 1 and k == 1:
        answer == 0
    print(answer)
    for j in range(0, answer):
        if (j+1+k)%n == 0:
            print(n),
        else:
            print((j+1+k)%n),
    print("\n")