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:
#!/usr/bin/python

import sys
#use ./ex1.py < input_ex1.py
    
def solve(N, K):
    print(N - K + int(K/2))
    out_string = ""
    for i in range (K+1, N+1):
        out_string += str(i)
        out_string += " "
    for i in range (int((K+1)/2), K):
        out_string += str(i)
        out_string += " "
    print(out_string)
    
    
    
def run():
    out = ""    
    T = int(input())
    for i in range(T):
        N, K = [int(x) for x in input().split()]
        solve(N, K)

run()