#include #include // #include // using Bint = boost::multiprecision::cpp_int; #define REP(i, n) for(int i = 0;i < n;i++) #define ll long long using namespace std; typedef pair P; typedef pair LP; const int dx[8] = {1, 0, -1, 0, 1, -1, -1, 1}; const int dy[8] = {0, 1, 0, -1, 1, 1, -1, -1}; const int INF = 1000000000; const ll LINF = 1000000000000000000;//1e18 const double PI = acos(-1.0); const double EPS = 1e-10; template inline bool chmax(T& a, T b) { if (a < b) { a = b; return true; } return false; } template inline bool chmin(T& a, T b) { if (a > b) { a = b; return true; } return false; } inline constexpr ll ceil_div(const ll a, const ll b) {return (a + b - 1) / b - !!((a + b - 1) % b < 0);}// return ceil(a/b) inline constexpr ll floor_div(const ll a, const ll b) {return a / b - !!(a % b < 0);}// return floor(a/b) /* ----------------------- DEBUG FUNCTION ---------------------------- */ #define DUMPOUT cerr void dump_function() { DUMPOUT << ' '; } void dump_function(bool a) { DUMPOUT << a; } void dump_function(int a) { DUMPOUT << a; } void dump_function(long long a) { DUMPOUT << a; } void dump_function(char a) { DUMPOUT << a; } void dump_function(string &a) { DUMPOUT << a; } void dump_function(double a) { DUMPOUT << a; } template void dump_function(const vector &); template void dump_function(const array &); template void dump_function(const pair &p); template void dump_function(const T (&)[size]); template void dump_function(const vector &a) { if(a.empty()) return; dump_function(a[0]); for(auto i = a.begin(); ++i != a.end();) { DUMPOUT << " "; dump_function(*i); } DUMPOUT << endl; } template void dump_function(const deque &a) { if(a.empty()) return; dump_function(a[0]); for(auto i = a.begin(); ++i != a.end();) { DUMPOUT << " "; dump_function(*i); } } template void dump_function(const array &a) { dump_function(a[0]); for(auto i = a.begin(); ++i != a.end();) { DUMPOUT << " "; dump_function(*i); } } template void dump_function(const pair &p) { DUMPOUT << '('; dump_function(p.first); DUMPOUT << ","; dump_function(p.second); DUMPOUT << ')'; } template void dump_function(set &x) { for(auto e : x) dump_function(e), DUMPOUT << " "; DUMPOUT << endl; } template void dump_function(multiset &x) { for(auto e : x) dump_function(e), DUMPOUT << " "; DUMPOUT << endl; } template void dump_function(const T (&a)[size]) { dump_function(a[0]); for(auto i = a; ++i != end(a);) { DUMPOUT << " "; dump_function(*i); } } template void dump_function(const T &a) { DUMPOUT << a; } int dump_out() { DUMPOUT << '\n'; return 0; } template int dump_out(const T &t) { dump_function(t); DUMPOUT << '\n'; return 0; } template int dump_out(const Head &head, const Tail &... tail) { dump_function(head); DUMPOUT << ' '; dump_out(tail...); return 0; } #ifdef DEBUG_ #define dump(x) \ DUMPOUT << #x << ": "; \ dump_function(x); \ DUMPOUT << endl; void dumps() {} template void dumps(const T &t) { dump_function(t); DUMPOUT << " "; } template void dumps(const Head &head, const Tail &... tail) { dump_function(head); DUMPOUT << ' '; dump_out(tail...); } #else #define dump(x) template void dumps(const T &...) {} #endif /* ----------------------- DEBUG FUNCTION ---------------------------- */ template struct Fp { long long val; constexpr Fp(long long v = 0) noexcept : val(v % MOD) { if (val < 0) val += MOD; } constexpr int getmod() const { return MOD; } constexpr Fp operator - () const noexcept { return val ? MOD - val : 0; } constexpr Fp operator + (const Fp& r) const noexcept { return Fp(*this) += r; } constexpr Fp operator - (const Fp& r) const noexcept { return Fp(*this) -= r; } constexpr Fp operator * (const Fp& r) const noexcept { return Fp(*this) *= r; } constexpr Fp operator / (const Fp& r) const noexcept { return Fp(*this) /= r; } constexpr Fp& operator += (const Fp& r) noexcept { val += r.val; if (val >= MOD) val -= MOD; return *this; } constexpr Fp& operator -= (const Fp& r) noexcept { val -= r.val; if (val < 0) val += MOD; return *this; } constexpr Fp& operator *= (const Fp& r) noexcept { val = val * r.val % MOD; return *this; } constexpr Fp& operator /= (const Fp& r) noexcept { long long a = r.val, b = MOD, u = 1, v = 0; while (b) { long long t = a / b; a -= t * b, swap(a, b); u -= t * v, swap(u, v); } val = val * u % MOD; if (val < 0) val += MOD; return *this; } constexpr bool operator == (const Fp& r) const noexcept { return this->val == r.val; } constexpr bool operator != (const Fp& r) const noexcept { return this->val != r.val; } friend constexpr istream& operator >> (istream& is, Fp& x) noexcept { is >> x.val; x.val %= MOD; if (x.val < 0) x.val += MOD; return is; } friend constexpr ostream& operator << (ostream& os, const Fp& x) noexcept { return os << x.val; } friend constexpr Fp modpow(const Fp& r, long long n) noexcept { if (n == 0) return 1; auto t = modpow(r, n / 2); t = t * t; if (n & 1) t = t * r; return t; } friend constexpr Fp modinv(const Fp& r) noexcept { long long a = r.val, b = MOD, u = 1, v = 0; while (b) { long long t = a / b; a -= t * b, swap(a, b); u -= t * v, swap(u, v); } return Fp(u); } }; template struct BiCoef { vector fact_, inv_, finv_; constexpr BiCoef() {} constexpr BiCoef(int n) noexcept : fact_(n, 1), inv_(n, 1), finv_(n, 1) { init(n); } constexpr void init(int n) noexcept { fact_.assign(n, 1), inv_.assign(n, 1), finv_.assign(n, 1); int MOD = fact_[0].getmod(); for(int i = 2; i < n; i++){ fact_[i] = fact_[i-1] * i; inv_[i] = -inv_[MOD%i] * (MOD/i); finv_[i] = finv_[i-1] * inv_[i]; } } constexpr T com(int n, int k) const noexcept { if (n < k || n < 0 || k < 0) return 0; return fact_[n] * finv_[k] * finv_[n-k]; } constexpr T fact(int n) const noexcept { if (n < 0) return 0; return fact_[n]; } constexpr T inv(int n) const noexcept { if (n < 0) return 0; return inv_[n]; } constexpr T finv(int n) const noexcept { if (n < 0) return 0; return finv_[n]; } constexpr T perm(int n, int k) const noexcept { if (n < k || n < 0 || k < 0) return 0; return fact_[n] * finv_[n-k]; } }; /* ----------------------------- MOD ----------------------------------- */ const int MOD = 1000000007; const int MOD2 = 998244353; using mint = Fp; BiCoef bc; // using vec = vector; // using mat = vector; /* ----------------------------- MOD ----------------------------------- */ /* ----------------------- AtCoder Library ---------------------------- */ // #include // using namespace atcoder; /* ----------------------- AtCoder Library ---------------------------- */ void solve(){ int N, M; cin >> N >> M; vector B(M); REP(i,M) cin >> B[i]; if(M <= 1){ cout << N - 1 << endl; return; } double ans = N - 1; double tmp = B[0] - 1 + N - B[M-1]; double sum = 0; for(int i=M-1;i>=1;i--){ sum += B.back() - B[i]; chmin(ans, tmp + sum / double(M - i) + double(M) / (M - i)); } printf("%.12lf\n", ans); } int main(){ cin.tie(0); ios::sync_with_stdio(false); solve(); // int T; cin >> T; REP(t,T) solve(); }