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() {
  int t;
  cin >> t;
  while (t--) {
    vector<long long> v;
    long long n, k;
    cin >> n >> k;
    bool dp[n + 1][k + 1];
    for (int i = 0; i <= n; i++) {
      dp[i][0] = 1;
    }
    for (int i = 1; i <= k; i++) dp[0][i] = 0;
    for (int i = 1; i <= n; i++) {
      for (int j = 1; j <= k; j++) {
        if (j - i >= 0) {
          dp[i][j] = dp[i - 1][j] or dp[i - 1][j - i];
        } else {
          dp[i][j] = dp[i - 1][j];
        }
      }
    }
    for (int i = 1; i < n + 1; i++) {
      if (dp[i][k] == 0) v.push_back(i);
      if (i > k) v.push_back(i);
    }
    if (v.size() == 0) {
      cout << 0 << endl;
      continue;
    }
    cout << v.size() << endl;
    for (int i = 0; i < v.size(); i++) cout << v[i] << " ";
    cout << endl;
  }
}
