#include<bits/stdc++.h>
#define Gc() getchar()
#define Me(x,y) memset(x,y,sizeof(x))
#define Mc(x,y) memcpy(x,y,sizeof(x))
#define d(x,y) ((m)*(x-1)+(y))
#define R(n) (rnd()%(n)+1)
#define Pc(x) putchar(x)
#define LB lower_bound
#define UB upper_bound
#define fi first
#define se second
#define eb emplace_back
#define all(x) x.begin(),x.end()
using namespace std;using ll=long long;using db=double;using lb=long db;using ui=unsigned;using ull=unsigned long long;using pii=pair<int,int>;
const int N=1e6+5,M=5e4+5,K=1000+5,mod=998244353,Mod=mod-1;const db eps=1e-9;const ll INF=1e18+7;mt19937 rnd(263082);
#define Tp template<typename T>
#define Ts template<typename T,typename... Ar>
namespace Debug{
	Tp void _debug(char* f,T t){cerr<<f<<'='<<t<<endl;}
	Ts void _debug(char* f,T x,Ar... y){while(*f!=',') cerr<<*f++;cerr<<'='<<x<<",";_debug(f+1,y...);}
	#ifdef LOCAL
	#define gdb(...) _debug((char*)#__VA_ARGS__,__VA_ARGS__)
	#else 
	#define gdb(...) void()
	#endif
}using namespace Debug;
int n,k;
db sum[N];
void init(){
	const int n=1e6;
	for(int i=1;i<=n;i++) sum[i]=sum[i-1]+log(i);
}
const db pis=log(2*acos(-1))/2;
db calc(int n){
	if(n<=1000000) return sum[n];
	return pis+log(n)*(n+0.5)-n;
}
db C(int x,int y){return calc(x)-calc(y)-calc(x-y);}
const db ln2=log(2),ln3=log(3);
void Solve(){
	int i,j;scanf("%d%d",&n,&k);
	if(n<=k){printf("%.9lf\n",log(3ll*k+1));return;}
	db l=0,r=2e9,mid;
	for(int i=1;i<=60;i++){
		mid=(l+r)/2;
		db tot=k+1;
		db w=mid-ln3*n;
		db lim=min(k,n*2/3+100);
		for(int j=lim;j>=0&&j>=lim-200&&tot<=3*k+1;j--){
			tot+=ceil(exp(w+ln2*j+C(n,j))-1);
		}
		(tot>3*k+1?r:l)=mid;
	}
	printf("%.9lf\n",l);
}
int main(){
	init();
	int t=1;
	scanf("%d",&t);
	while(t--) Solve();
	cerr<<clock()*1.0/CLOCKS_PER_SEC<<'\n';
}