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;
int main() {
  long long q;
  scanf("%lld", &q);
  while (q--) {
    long long j = 0, i = 0, p = 0, k = 0, c = 0, s = 0, m, t, a, b;
    vector<long long> w;
    cin >> a >> b;
    for (i = 1; i <= b; i++) {
      c += i;
      if (c >= b)
        break;
      else
        w.push_back(i);
    }
    s = a - b;
    p = w.size();
    printf("%lld\n", s + p);
    for (long long i = 0; i < w.size(); i++) {
      cout << w[i] << " ";
    }
    for (j = b + 1; j <= a; j++) printf("%lld ", j);
    printf("\n");
  }
  return 0;
}
