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>
#define ll long long
using namespace std;
int n, k, v[1010];

int main() {
    cin.tie(0);
    cout.tie(0);
    ios::sync_with_stdio(0);
    int t;
    cin >> t;

    while (t--) {
        cin >> n >> k;
        int dim = 0;
        for (int i = k + 1; i <= n; i++)
            v[dim++] = i;
        for (int i = k / 2 + k % 2; i < k; i++)
            v[dim++] = i;
        cout << dim << "\n";
        for (int i = 0; i < dim; i++)
            cout << v[i] << " ";
        cout << "\n";
    }
    return 0;
}