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 PYTHON):

Solution:
def solve(n, k):
    x = k / 2 + (k & 1)
    ans = []
    for i in xrange(x, n+1):
        if i == k: continue
        ans += i,
    return ans

for _ in xrange(int(raw_input())):
    n, k = map(int, raw_input().split())
    ans = solve(n, k)
    print len(ans)
    print ' '.join(map(str, ans))