#include #if __has_include() #endif using namespace std; #define RD(T,...) T __VA_ARGS__;lin(__VA_ARGS__) #define LL(...) RD(ll,__VA_ARGS__) #define DD(...) RD(dd,__VA_ARGS__) #define RDVL(T,n,...) vec__VA_ARGS__;fe(refs(__VA_ARGS__),e)e.get().resizes(n);lin(__VA_ARGS__) #define VL(n,...) RDVL(ll,n,__VA_ARGS__) #define FO(n) for(ll IJK=n;IJK-->0;) #define fo(i,...) for(auto[i,i##stop,i##step]=for_range(0,__VA_ARGS__);ivoid pp(const auto&...a){[[maybe_unused]]const char*c="";((o<(a...);} #define entry defpp void main();void main2();}int main(){my::io();my::main();}namespace my{ #define multi_test_cases LL(T);FO(T)main2();}void main2(){ namespace my{ void io(){cin.tie(nullptr)->sync_with_stdio(0);cout<constexpr auto for_range(T s,T b){T a=0;if(s)swap(a,b);return array{a-s,b,1-s*2};} templateconstexpr auto for_range(T s,T a,T b,T c=1){return array{a-s,b,(1-s*2)*c};} void lin(auto&...a){(cin>>...>>a);} constexpr ll size10(auto x){x|=1;ll r=0;while(x>0)x/=10,++r;return r;} templateconstexpr ll maxsize10(){return size10(numeric_limits::max());} bool amin(auto&a,const auto&b){return bstruct infinity{ templatestatic constexpr T ones(size_t n){return n?ones(n-1)*10+1:0;} templateconstexpr operator T()const{return ones(maxsize10())*(1-is_negative*2);} templateconstexpr operator T()const{return static_cast(*this);} }; constexpr infinity oo; templateusing pack_back_t=tuple_element_t>; } namespace my{ templateistream&operator>>(istream&i,vector&v){fe(v,e)i>>e;return i;} templateconstexpr int depth=0; templatestruct core_t_helper{using type=T;}; templateusing core_t=core_t_helper::type; templatestruct vec; templatestruct hvec_helper{using type=vec::type>;}; templatestruct hvec_helper<0,T>{using type=T;}; templateusing hvec=hvec_helper::type; templatestruct vec:vector{ static constexpr int D=depth+1; using C=core_t; using vector::vector; void resizes(const auto&...a){if constexpr(sizeof...(a)==D)*this=make(a...,C{});else{ }} static auto make(ll n,const auto&...a){ if constexpr(sizeof...(a)==1)return vec(n,array{a...}[0]); else { } } auto&emplace_front(auto&&...a){this->emplace(this->begin(),std::forward(a)...);return*this;} templateauto min(ll l,ll r)const{T res=oo;fo(i,l,r)amin(res,(*this)[i]);return res;} }; templaterequires(sizeof...(A)>=2)vec(const A&...a)->vec>>; } namespace my{entry void main(){ multi_test_cases LL(N); DD(X); VL(N,h,a); h.emplace_front(0); auto calc=[&](ll k)->dd{ if(a.min(0,k)<=a[k])return oo; dd res=0; dd su=0; fo(i,k){ dd d=h[i+1]-h[i]; dd th=acos(dd(a[k])/a[i]); res+=d/std::sin(th)*a[i]; su+=d/tan(th); } if(X/2-su<0)return oo; res+=(X/2-su)*a[k]; return res*2; }; dd ans=oo; fo(i,N)amin(ans,calc(i)); pp(ans); }}