#include #include // cout, endl, cin #include // string, to_string, stoi #include // vector #include // min, max, swap, sort, reverse, lower_bound, upper_bound #include // pair, make_pair #include // tuple, make_tuple #include // int64_t, int*_t #include // printf #include // map #include // queue, priority_queue #include // set #include // stack #include // deque #include // unordered_map #include // unordered_set #include // bitset #include // isupper, islower, isdigit, toupper, tolower #include #include using namespace std; using namespace atcoder; #define rep(i, n) for (int i = 0; i < (int)(n); i++) #define repi(i, a, b) for (int i = (int)(a); i < (int)(b); i++) typedef long long ll; typedef unsigned long long ull; const ll inf=1e18; using graph = vector > ; using P= pair; using vi=vector; using vvi=vector; using vll=vector; using vvll=vector; using vp=vector

; using vpp=vector; //string T="ABCDEFGHIJKLMNOPQRSTUVWXYZ"; //string S="abcdefghijklmnopqrstuvwxyz"; //g++ main.cpp -std=c++14 -I . //cout < par, siz; UnionFind(int n) : par(n, -1) , siz(n, 1) { } int root(int x) { if (par[x] == -1) return x; else return par[x] = root(par[x]); } bool issame(int x, int y) { return root(x) == root(y); } bool unite(int x, int y) { x = root(x), y = root(y); if (x == y) return false; if (siz[x] < siz[y]) swap(x, y); par[y] = x; siz[x] += siz[y]; return true; } int size(int x) { return siz[root(x)]; } }; int gcd(int x,int y){ if(y==0)return x; return gcd(y,x%y); } ll lcm(ll x,ll y){ return ll(x/gcd(x,y))*y; } template bool chmin(T& a, T b) { if (a > b) { a = b; return true; } else return false; } template bool chmax(T& a, T b) { if (a < b) { a = b; return true; } else return false; } // https://youtu.be/L8grWxBlIZ4?t=9858 // https://youtu.be/ERZuLAxZffQ?t=4807 : optimize // https://youtu.be/8uowVvQ_-Mo?t=1329 : division const ll mod =1e9+7; struct mint { ll x; // typedef long long ll; mint(ll x=0):x((x%mod+mod)%mod){} mint operator-() const { return mint(-x);} mint& operator+=(const mint a) { if ((x += a.x) >= mod) x -= mod; return *this; } mint& operator-=(const mint a) { if ((x += mod-a.x) >= mod) x -= mod; return *this; } mint& operator*=(const mint a) { (x *= a.x) %= mod; return *this;} mint operator+(const mint a) const { return mint(*this) += a;} mint operator-(const mint a) const { return mint(*this) -= a;} mint operator*(const mint a) const { return mint(*this) *= a;} mint pow(ll t) const { if (!t) return 1; mint a = pow(t>>1); a *= a; if (t&1) a *= *this; return a; } // for prime mod mint inv() const { return pow(mod-2);} mint& operator/=(const mint a) { return *this *= a.inv();} mint operator/(const mint a) const { return mint(*this) /= a;} }; istream& operator>>(istream& is, const mint& a) { return is >> a.x;} ostream& operator<<(ostream& os, const mint& a) { return os << a.x;} // combination mod prime // https://www.youtube.com/watch?v=8uowVvQ_-Mo&feature=youtu.be&t=1619 struct combination { vector fact, ifact; combination(int n):fact(n+1),ifact(n+1) { //assert(n < mod); fact[0] = 1; for (int i = 1; i <= n; ++i) fact[i] = fact[i-1]*i; ifact[n] = fact[n].inv(); for (int i = n; i >= 1; --i) ifact[i-1] = ifact[i]*i; } mint operator()(int n, int k) { if (k < 0 || k > n) return 0; return fact[n]*ifact[k]*ifact[n-k]; } mint p(int n, int k) { return fact[n]*ifact[n-k]; } } c(10000050); using vm=vector ; using vvm=vector ; ll sqrt_(ll x) { ll l = 0, r = ll(3e9)+1; while (l+1=0 && y>=0 && x; using vve =vector; void comp(vll&a){ sets(a.begin(),a.end()); int cnt=0; mapd; for(auto y:s)d[y]=cnt++; for(auto&y:a)y=d[y]; } int main(){cin.tie(0); ios::sync_with_stdio(false); int n,m; cin >> n >> m; vi b(m);rep(i,m)cin >> b[i]; vector dp(m); dp[m-1]=n-b[m-1]; double sum=dp[m-1]; for(int i=m-2; i>=0; i--){ dp[i]=n-b[i]; double now=1.0*m/(m-1-i)+sum/(m-1-i); chmin(dp[i],now); sum+=dp[i]; } double ans=n-1; chmin(ans,dp[0]+b[0]-1); cout << setprecision(20); cout << ans << endl; }