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 t, n, k;

int main() {
  cin >> t;
  while (t--) {
    cin >> n >> k;
    cout << n - k + k / 2 << endl;
    for (int i = n; i > k; --i) {
      cout << i << " ";
    }
    for (int i = k - 1; i > (k - 1) / 2; --i) {
      cout << i << " ";
    }
    cout << endl;
  }
  return 0;
}