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 CPP):

Solution:
#include <iostream>
using namespace std;
int main() {
    int t, n, k;
    cin >> t;
    while (t--) {
        cin >> n >> k;
        cout << n - k + k / 2 << "\n";
        for (int i = k + 1; i <= n; i++) {
            cout << i << " ";
        }
        for (int i = (k + 1) / 2; i < k; i++) {
            cout << i << " ";
        }
        cout << "\n";
    }
}