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:
for _ in range(int(input())):
  
  n_k = list(map(int, input().strip().split()))
  
  n = n_k[0]
  k = n_k[1]
  answ = []
  for i in range(k+1, n + 1):
    answ.append(i)
  bad = []
  for i in range(0, k+1):
    bad.append(0)
  bad[-1] = 1
  bad[0] = 1

  for i in range(k, -1, -1):
    if bad[i] == 0:
      answ.append(i)
      bad[k-i] = 1
  print(len(answ))
  answ = list(map(str, answ))
  print(" ".join(answ))