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
#include <bits/stdc++.h>
using namespace std;
long long gcd(long long a, long long b) { return b ? gcd(b, a % b) : a; }
long long lcm(long long a, long long b) { return a * b / gcd(a, b); }
void solve() {
  int n;
  cin >> n;
  int k;
  cin >> k;
  vector<int> a;
  for (int i = k + 1; i < n + 1; i++) a.push_back(i);
  int sum = 0;
  int i = 1;
  while (sum + i < k) {
    sum += i;
    a.push_back(i);
    i++;
  }
  cout << a.size() << '\n';
  for (int i = 0; i < a.size(); i++) {
    cout << a[i] << ' ';
  }
  cout << '\n';
}
int main() {
  ios::sync_with_stdio(0);
  cin.tie(0);
  int TT = 1;
  cin >> TT;
  for (int i = 0; i < TT; i++) solve();
  return 0;
}
