#include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #define _overload3(_1,_2,_3,name,...) name #define _rep(i,n) repi(i,0,n) #define repi(i,a,b) for(ll i=a;i=b;--i) #define rrep(...) _overload3(__VA_ARGS__,rrepi,_rrep,)(__VA_ARGS__) #define all(x) (x).begin(),(x).end() #define PRINT(V) cout << V << "\n" #define SORT(V) sort((V).begin(),(V).end()) #define RSORT(V) sort((V).rbegin(), (V).rend()) using namespace std; using ll = long long; templatebool chmax(T &a, const T &b) { if (abool chmin(T &a, const T &b) { if (b void cins(itr first,itr last){ for (auto i = first;i != last;i++){ cin >> (*i); } } template void array_output(itr start,itr goal){ string ans = "",k = " "; for (auto i = start;i != goal;i++) ans += to_string(*i)+k; if (!ans.empty()) ans.pop_back(); PRINT(ans); } ll gcd(ll a, ll b) { return a ? gcd(b%a,a) : b; } const ll INF = 1e18; const ll MOD = 1000000007; const ll MOD2 = 998244353; const ll MOD3 = 1e6; const ll EPS = 1e-10; int sgn(const double a){ return (a < -EPS ? -1 : (a > EPS ? +1 : 0)); } typedef pair pi; typedef pair P; typedef tuple tri; typedef pair point; typedef complex Point; typedef string::const_iterator State; const ll MAX = 105; constexpr ll nx[4] = {-1,0,1,0}; constexpr ll ny[4] = {0,1,0,-1}; const double PI = 3.1415926535; int main(){ ll n,l; scanf("%lld %lld",&n,&l); vector coss(n),sins(n); rep(i,n){ double t; scanf("%lf",&t); coss[i] = cos(2*PI*t/(double)l); sins[i] = sin(2*PI*t/(double)l); } double sumsin = 0.0,sumcos = 0.0; rep(i,n){ sumsin += sins[i]; sumcos += coss[i]; } double ans = 0.0,nowsin = 0.0,nowcos = 0.0; rep(i,n-1){ nowsin += (n-i-2)*sins[i+1]; nowcos += (n-i-2)*coss[i+1]; } rep(i,n){ ans += nowsin*coss[i]-nowcos*sins[i]; nowsin = nowsin+sumsin-(n-1)*sins[(i+1)%n]-sins[i]; nowcos = nowcos+sumcos-(n-1)*coss[(i+1)%n]-coss[i]; } ll k = n*(n-1)*(n-2)/6; printf("%.10lf\n",ans/(double)k/2.0); }