This submission is migrated from previous version of oj.uz, which used different machine for grading. This submission may have different result if resubmitted.
#include<iostream>
#include<vector>
#include<map>
#include<set>
#include<cassert>
#include<cassert>
#include<unordered_map>
#include<unordered_set>
#include<functional>
#include<queue>
#include<stack>
#include<cstring>
#include<algorithm>
#include<cmath>
#include<sstream>
#include<iomanip>
#include<cstdio>
#include<cstdlib>
#include<numeric>
using namespace std;
#define all(x) (x).begin(), (x).end()
#define pb push_back
#define xx first
#define yy second
#define sz(x) (int)(x).size()
#define gc getchar
#define IO ios_base::sync_with_stdio(false);cin.tie(0);cout.tie(0)
#define mp make_pair
#ifndef ONLINE_JUDGE
# define LOG(x) (cerr << #x << " = " << (x) << endl)
#else
# define LOG(x) ((void)0)
#endif
typedef long long ll;
typedef unsigned long long ull;
typedef long double ld;
const double PI=3.1415926535897932384626433832795;
const ll INF = 1LL<<62;
const ll MINF = -1LL<<62;
template<typename T> T getint() {
T val=0;
char c;
bool neg=false;
while((c=gc()) && !(c>='0' && c<='9')) {
neg|=c=='-';
}
do {
val=(val*10)+c-'0';
} while((c=gc()) && (c>='0' && c<='9'));
return val*(neg?-1:1);
}
double dp[100001];
int cnt[100001];
int main() {
IO;
int n,k,it=0;
cin>>n>>k;
double L=0, R=1e9;
while(it++<80) {
double mid=(L+R)/2;
dp[0]=0.0;
cnt[0]=0;
for(int i=0;i<=n;++i) {
dp[i]=0.0;
}
for(int i=0;i<=n;++i) {
for(int j=1;i+j<=n;j++) {
double akt=dp[i]+double(j)/double(n-i)-mid;
if(dp[i+j]<akt) {
dp[i+j]=akt;
cnt[i+j]=cnt[i]+1;
}
}
}
//cerr<<mid<<" "<<dp[n]<<" "<<cnt[n]<<"?"<<k<<"\n";
if(cnt[n]<=k) {
R=mid;
}else {
L=mid;
}
}
cout<<fixed<<setprecision(10);
cout<<dp[n]+L*cnt[n]<<"\n";
return 0;
}
/*
double dp[3001][3001];
int main() {
IO;
int n,k;
cin>>n>>k;
dp[n][0]=0.0;
for(int i=1;i<=k;++i) {
for(int j=0;j<=n;++j) {
for(int l=0;l<=n/i && j+l<=n;l++) {
dp[j][i]=max(dp[j][i], dp[j+l][i-1]+(l>0?(double)l/(double)(j+l):0));
}
}
}
cout<<fixed<<setprecision(10);
cout<<dp[0][k]<<"\n";
return 0;
}*/
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