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 <bits/stdc++.h>
#include <unordered_map>
#include <chrono>
#include <random>

#define mp make_pair
#define pb push_back
#define ll long long
#define ll_MAX 1e18

ll MOD = 1e18 + 1;

using namespace std;

int main() {

    ios::sync_with_stdio(false);
    cin.tie(NULL);

    int nan; cin >> nan;

    for (int qq = 0; qq < nan; qq++) {

        int n, k; cin >> n >> k;

        cout << (n - k) + (k-(k+1)/2) << endl;
        for (int i = (k+1)/2; i < k; i++) {
            cout << i << " ";
        }
        for (int i = k + 1; i <= n; i++) {
            cout << i << " ";
        }
        cout << endl;
    }


    return 0;
}