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 sys

t = int(sys.stdin.readline().strip())

for _ in range(t):
    n, k = map(int, sys.stdin.readline().split())
    a = []
    b = []
    for j in range(k+1, n+1):
        a.append(j)
        b.append(j)
    for j in range(1, k, 2):
        a.append(j)
    for i in range(2, k, 2):
        b.append(i)
    if k%2 == 1:
        if len(a) > len(b):
            print(len(a))
            for j in a:
                print(j, end=' ')
        else:
            print(len(b))
            for j in b:
                print(j, end= ' ')
    else:
        print(len(a))
        for j in a:
            print(j, end=' ')
    print(' ')