Description：

Solution：

Code：

#include<algorithm>

#include<iostream>

#include<cstdlib>

#include<cstdio>

#include<cmath>

#include<cctype>

#include<cstring>

using namespace std;

int n;

double alpha;

#define MAXN 510

double r[MAXN],h[MAXN];

struct circ

{

	double x,r;

}c[MAXN];

struct line

{

	double k,b;

	double l,r;

}l[MAXN];

const double eps = 1e-10;

line build_line(circ a,circ b)

{

	if((a.x - a.r <= b.x - b.r && a.x + a.r >= b.x + b.r) || (b.x - b.r <= a.x - a.r && b.x + b.r >= a.x + a.r))

	{

		return (line){0,0,0,0};

	}

	line res;

	if(fabs(a.r - b.r) <= eps)

	{

		res.l = a.x;res.r = b.x;

		res.k = 0;res.b = a.r;

		return res;

	}

	else

	{

		double x = (b.r * a.x - b.x * a.r) / (b.r - a.r);

		double xa,ya,xb,yb;

		if(fabs(a.x - x) > eps)xa = a.x - a.r * a.r / (a.x - x);

		else xa = a.x;

		ya = sqrt(a.r * a.r - (a.x - xa) * (a.x - xa));

		if(fabs(b.x - x) > eps)xb = b.x - b.r * b.r / (b.x - x);

		else xb = b.x;

		yb = sqrt(b.r * b.r - (b.x - xb) * (b.x - xb));

		res.l = xa;res.r = xb;

		res.k = (ya - yb) / (xa - xb);

		res.b = yb - xb * res.k;

		return res;

	}

}

double f(double x)

{

	double res = 0;

	for(int i = 1;i <= n;++i)

	{

		if(x <= c[i].x - c[i].r || x > c[i].x + c[i].r)continue;

		res = max(res,sqrt(c[i].r * c[i].r - (x - c[i].x) * (x - c[i].x)));

	}

	for(int i = 1;i < n;++i)

	{

		if(x < l[i].l || x > l[i].r)continue;

		res = max(res,l[i].k * x + l[i].b);

	}

	return res;

}

double simpson(double l,double r)

{

	return (r - l) * (f(l) + 4 * f((l + r) / 2) + f(r)) / 6;

}

double solve(double l,double r,double k)

{

	double mid = (l + r) / 2;

	double L = simpson(l,mid),R = simpson(mid,r);

	if(fabs(L + R - k) <= eps)return k;

	else return solve(l,mid,L) + solve(mid,r,R);

}

int main()

{

	scanf("%d%lf",&n,&alpha);

	for(int i = 1;i <= n + 1;++i)scanf("%lf",&h[i]);

	for(int i = 1;i <= n;++i)scanf("%lf",&r[i]);

	r[++n] = 0;

	double H = 0;

	for(int i = 1;i <= n;++i)

	{

		H += h[i];

		c[i].x = H / tan(alpha);

		c[i].r = r[i];

	}

	for(int i = 1;i < n;++i)l[i] = build_line(c[i],c[i + 1]);

	double l = 10000000,r = 0;

	for(int i = 1;i <= n;++i)

	{

		l = min(l,c[i].x - c[i].r);

		r = max(r,c[i].x + c[i].r);

	} 

	printf("%.2lf\n",solve(l,r,simpson(l,r)) * 2);

	return 0;

}