#include //#include using namespace std; //g++ hoge.cpp (-std=c++17) -I . で実行 typedef long long ll; typedef pair prl; typedef vector vcl; typedef map mapl; typedef unordered_map umap; #define pb push_back #define all(v) v.begin(), v.end() #define rep(i,a,b) for(ll i=a;i<=b;i++) #define repi(i,a,b) for(int i=a;i<=b;i++) #define repr(i,a,b) for(ll i=a;i>=b;i--) #define reps(i,v) for(ll i=0;i void chmin(T &a, const T &b) { a = min(a, b); } template void chmax(T &a, const T &b) { a = max(a, b); } ll myceil(ll a, ll b) { return (a+b-1) / b; } //const ll mod = 1e9+7; //const ll mod = 998244353; //typedef modint1000000007 mint; //typedef modint998244353 mint; //typedef modint mint //cout << sum.val() << endl; //mint::set_mod(mod); modが固定でないとき ll n; const ll max_n = 500005; double m,l,t[max_n],a[max_n],s[max_n],c[max_n]; double ss[max_n],sc[max_n],ss2[max_n],sc2[max_n]; int main() { // your code goes here cin >> n >> l; double pi = atan2(0.0, -1.0); rep(i,1,n){ scanf("%lf",&t[i]); a[i] = 2.0*pi*t[i]/l; s[i] = sin(a[i]); ss[i] = ss[i-1] + s[i]; c[i] = cos(a[i]); sc[i] = sc[i-1] + c[i]; } m = n; sc2[1] = (2.0-m) * c[1]; double ar1 = sc2[1] * s[2]; rep(i,3,n){ sc2[i-1] = sc2[i-2] + 2.0 * sc[i-2] + (2.0-m) * c[i-1]; ar1 += sc2[i-1] * s[i]; } ss2[1] = (2.0-m) * s[1]; double ar2 = ss2[1] * c[2]; rep(i,3,n){ ss2[i-1] = ss2[i-2] + 2.0 * ss[i-2] + (2.0-m) * s[i-1]; ar2 += ss2[i-1] * c[i]; } ll ss = n * (n-1) * (n-2) / 6; fprint((ar2-ar1)/((double)ss*2.0)); return 0; }