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:
def solve_tc():
    n, k = map(int, input().split())
    ans = []
    if k % 2 == 1:
        ki = k//2 + 1
    else:
        ki = k//2
    for i in range(ki, n+1):
        if k != i:
            ans.append(i)
    return ans, len(ans)


t = int(input())
while t > 0:
    t -= 1
    m, l = solve_tc()
    print(str(l))
    print(" ".join(list(map(str, m))))