POJ 3744

#include <iostream>
#include <algorithm>
#include <cstdio>
#include <cstring>
using namespace std;

int pos[15];

struct matrix{
	double m[3][3];
};
matrix per,pt,ps;

matrix operator *(matrix a,matrix b){
	matrix c;
	for(int i=1;i<=2;i++){
		for(int j=1;j<=2;j++){
			c.m[i][j]=0;
			for(int k=1;k<=2;k++)
			c.m[i][j]+=(a.m[i][k]*b.m[k][j]);
		}
	}
	return c;
}

matrix quick(int k){
	matrix ans=per,p=pt;
	while(k){
		if(k&1) ans=ans*p;
		k>>=1;
		p=p*p;
	}
	return ans;
}

int main(){
	int n; double p;
	while(scanf("%d%lf",&n,&p)!=EOF){
		memset(per.m,0,sizeof(per.m));
		per.m[1][1]=per.m[2][2]=1;
		memset(pt.m,0,sizeof(pt.m));
		pt.m[1][1]=p;pt.m[2][1]=1; pt.m[1][2]=1-p;
		memset(ps.m,0,sizeof(ps.m));
		ps.m[1][1]=p; ps.m[2][1]=1;
		for(int i=1;i<=n;i++)
		scanf("%d",&pos[i]);
		sort(pos+1,pos+n+1);
		if(pos[1]==1){
			printf("%.7lf\n",0);
			continue;
		}
		pos[0]=0;
		matrix tmp;
		double ans=1;
		for(int i=1;i<=n;i++){
			int g=pos[i]-1-pos[i-1]-1;
			if(g>0){
				tmp=quick(g-1);
				tmp=tmp*ps;
				ans=ans*tmp.m[1][1];
			}
			if(pos[i+1]==pos[i]+1){
				ans=0;
				break;
			}
			ans*=(1-p);
		}
		printf("%.7lf\n",ans);
	}
	return 0;
}