#include using namespace std; #pragma GCC optimize("O3") #define rep(i,n) for(ll i=0;i=0;i--) #define perl(i,r,l) for(ll i=r-1;i>=l;i--) #define fi first #define se second #define ins insert #define pqueue(x) priority_queue,greater> #define all(x) (x).begin(),(x).end() #define CST(x) cout<; using vvl=vector>; using pl=pair; using vpl=vector; using vvpl=vector; const ll MOD=1000000007; const ll MOD9=998244353; const int inf=1e9+10; const ll INF=4e18; const ll dy[9]={1,0,-1,0,1,1,-1,-1,0}; const ll dx[9]={0,1,0,-1,1,-1,1,-1,0}; template inline bool chmax(T &a, T b) { return ((a < b) ? (a = b, true) : (false)); } template inline bool chmin(T &a, T b) { return ((a > b) ? (a = b, true) : (false)); } vector gauss_jordan(const vector> &A,const vector &b){ int n=A.size(); vector> B(n,vector(n+1)); rep(i,n){ rep(j,n)B[i][j]=A[i][j]; } rep(i,n)B[i][n]=b[i]; rep(i,n){ int pivot=i;//係数が0になることを防ぐ for(int j=i;jabs(B[pivot][i]))pivot=j; } swap(B[i],B[pivot]); for(int j=i+1;j<=n;j++)B[i][j]/=B[i][i]; rep(j,n){ if(i!=j){ for(int k=i+1;k<=n;k++)B[j][k]-=B[j][i]*B[i][k]; } } } vector x(n); rep(i,n)x[i]=B[i][n]; return x; } int main(){ ll n,m;cin >> n >> m; using vd=vector; vd c(n); for(ll i=1;i> c[i]; vector mat(n,vd(n)); vd b(n); rep(i,n-1){ mat[i][i]-=1; double sum=0; rep(_,m){ ll to=i+_+1; if(to>n-1){ ll f=to-(n-1); to-=f*2; } mat[i][to]+=1.0/m; sum+=c[to]; } b[i]=-sum/m; } mat[n-1][n-1]=1;b[n-1]=0; auto f=gauss_jordan(mat,b); CST(10); //rep(i,n)cout << f[i] << endl; vd dp(n,INF);dp[n-1]=0; per(i,n-1){ if(i+m>=n-1){ dp[i]=0;continue; } double sum=0; double mx=INF; for(ll j=i+1;j<=i+m;j++){ sum+=dp[j]+c[j]; chmin(mx,f[j]+c[j]); } dp[i]=min(sum/m,mx); } cout << dp[0] << endl; }