SP4060 KPGAME - A game with probability

#include<bits/stdc++.h>
#define Tp template<typename Ty>
#define Ts template<typename Ty,typename... Ar>
#define W while
#define I inline
#define RI register int
#define LL long long
#define Cn const
#define CI Cn int&
#define gc getchar
#define D isdigit(c=gc())
#define pc(c) putchar((c))
#define min(x,y) ((x)<(y)?(x):(y))
#define max(x,y) ((x)>(y)?(x):(y))
using namespace std;
namespace Debug{
	Tp I void _debug(Cn char* f,Ty t){cerr<<f<<'='<<t<<endl;}
	Ts I void _debug(Cn char* f,Ty x,Ar... y){W(*f!=',') cerr<<*f++;cerr<<'='<<x<<",";_debug(f+1,y...);}
	Tp ostream& operator<<(ostream& os,Cn vector<Ty>& V){os<<"[";for(Cn auto& vv:V) os<<vv<<",";os<<"]";return os;}
	#define gdb(...) _debug(#__VA_ARGS__,__VA_ARGS__)
}using namespace Debug;
namespace FastIO{
	Tp I void read(Ty& x){char c;int f=1;x=0;W(!D) f=c^'-'?1:-1;W(x=(x<<3)+(x<<1)+(c&15),D);x*=f;}
	Ts I void read(Ty& x,Ar&... y){read(x),read(y...);}
	Tp I void write(Ty x){x<0&&(pc('-'),x=-x,0),x<10?(pc(x+'0'),0):(write(x/10),pc(x%10+'0'),0);}
	Tp I void writeln(Cn Ty& x){write(x),pc('\n');}
}using namespace FastIO;
Cn int N=1e6+10;
int Tt,n;double A,B,f[N][2],p,q;
int main(){
	RI i;read(Tt);W(Tt--){
		for(read(n),scanf("%lf%lf",&A,&B),assert(0.5<=A&&A<=1&&0.5<=B&&B<=1),f[0][0]=0,f[0][1]=1,i=1;i<=min(n,1000);i++)
			f[i-1][1]>f[i-1][0]?(p=A,q=B):(p=1-A,q=1-B),f[i][0]=(f[i-1][0]*q*(1-p)+f[i-1][1]*p)/(1-(1-q)*(1-p)),f[i][1]=f[i][0]*(1-q)+f[i-1][0]*q;
		printf("%.6lf\n",f[min(n,1000)][0]);
	}return 0;
}