1 uses math;
 2 const
 3     maxn=510;
 4     eps=1e-7;
 5 var
 6     x,rr,fx1,fy1,fx2,fy2,k:array[0..maxn]of double;
 7     n:longint;
 8     a,l,r,m,fl,fr,fm:double;
 9
10 function simpson(l,r,fl,fr,fm:double):double;
11 begin
12     exit((r-l)/6*(fl+fr+4*fm));
13 end;
14
15 function f(a:double):double;
16 var
17     i:longint;
18 begin
19     f:=0;
20     for i:=1 to n do
21         begin
22             if abs(a-x[i])<rr[i] then f:=max(f,sqrt(sqr(rr[i])-sqr(a-x[i])));
23             if (a>fx1[i]) and (a<fx2[i]) then f:=max(f,fy1[i]+(a-fx1[i])*k[i]);
24         end;
25 end;
26
27 function area(l,m,r,fl,fm,fr,pre:double):double;
28 var
29     ll,rr,fll,frr,ls,rs:double;
30 begin
31     ll:=(l+m)/2;rr:=(m+r)/2;fll:=f(ll);frr:=f(rr);
32     ls:=simpson(l,m,fl,fm,fll);rs:=simpson(m,r,fm,fr,frr);
33     if abs(ls+rs-pre)<eps then exit(pre);
34     exit(area(l,ll,m,fl,fll,fm,ls)+area(m,rr,r,fm,frr,fr,rs));
35 end;
36
37 procedure main;
38 var
39     i:longint;
40 begin
41     read(n,a);a:=1/tan(a);
42     for i:=1 to n+1 do read(x[i]);
43     for i:=2 to n+1 do x[i]:=x[i]+x[i-1];
44     for i:=1 to n+1 do x[i]:=x[i]*a;
45     for i:=1 to n do read(rr[i]);
46     r:=x[n+1];l:=x[n+1];
47     for i:=1 to n do
48         begin
49             if x[i]-rr[i]<l then l:=x[i]-rr[i];
50             if x[i]+rr[i]>r then r:=x[i]+rr[i];
51         end;
52     for i:=1 to n do
53         if (x[i]-rr[i]<x[i+1]-rr[i+1]) and (x[i]+rr[i]<x[i+1]+rr[i+1]) then
54         begin
55             fx1[i]:=x[i]+rr[i]*(rr[i]-rr[i+1])/(x[i+1]-x[i]);fy1[i]:=sqrt(sqr(rr[i])-sqr(fx1[i]-x[i]));
56             fx2[i]:=x[i+1]+rr[i+1]*(rr[i]-rr[i+1])/(x[i+1]-x[i]);fy2[i]:=sqrt(sqr(rr[i+1])-sqr(fx2[i]-x[i+1]));
57             if abs(fx2[i]-fx1[i])>eps then k[i]:=(fy2[i]-fy1[i])/(fx2[i]-fx1[i]);
58         end;
59     m:=(l+r)/2;fl:=f(l);fr:=f(r);fm:=f(m);
60     writeln(2*area(l,m,r,fl,fm,fr,simpson(l,r,fl,fr,fm)):0:2);
61 end;
62
63 begin
64     main;
65 end.