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 sys
import math

def read_ints():
    inp = input().split()
    inp = [int(x) for x in inp]
    return inp

def read_strings():
    inp = input()
    s = [inp[i] for i in range(len(inp))]
    return s

t = int(input())
for _ in range(t):
    nk = read_ints()
    n = nk[0]
    k = nk[1]
    ans = []
    if n > k:
        for i in range(k+1, n+1):
            ans.append(i)
    if k % 2 == 0:
        st = k//2
    else:
        st = k//2+1

    for i in range(st, k):
        ans.append(i)
    ans = [str(a) for a in ans]
    print(len(ans))
    print(' '.join(ans))