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 $T$ ($1 \le T \le 100$).

Each of the next $T$ lines contains two integers $n$ and $k$ ($1 \le k \le n \le 1000$) — 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.

Samples

3
3 2
5 3
1 1

2
3 1 
3
4 5 2 
0