#include <map>
#include <set>
#include <array>
#include <cmath>
#include <deque>
#include <bitset>
#include <random>
#include <string>
#include <vector>
#include <cassert>
#include <complex>
#include <iomanip>
#include <iostream>
#include <algorithm>
#include <unordered_map>
#include <unordered_set>

using namespace std;


using ld = double;

const ld PI = atan2l(0, -1);

ld fact(int x) {
    if (x == 0) return 0;
    return log(2 * PI * x) / 2 + x * log(x) - x;
}

ld C(int n, int k) {
    return fact(n) - fact(k) - fact(n - k);
}

ld add(ld p, ld q) {
    if (p > q) swap(p, q);
    return q + log(1 + exp(p - q));
}

const int D = 100;

void solve() {
    int n, k;
    cin >> n >> k;
    ld cur = 0;
    int len = (n + D - 1) / D;
    k = min(k, n);
    for (int i = k + 1; i <= n; i += len) {
        int L = i, R = min(n + 1, i + len);
        ld res = C(n, L);
        if (R - L < 50) {
            res += L * log(2) + log((1ll << (R - L)) - 1);
        } else {
            res += R * log(2);
        }
        cur = add(cur, res);
    }
    ld ans = log(3 * k + 1) + cur;
    /// ans += n * log(3);
    cout << ans << "\n";
}

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

  cout << fixed << setprecision(20);

  int tst;
  cin >> tst;
  while (tst--) {
    solve();
  }

  
  return 0;
}