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 <bits/stdc++.h>
//#pragma GCC optimize("unroll-loops")
//#pragma GCC optimize("-O3")
//#pragma GCC optimize("Ofast")
//#pragma GCC optimize("fast-math")
//#pragma GCC optimize("no-stack-protector")
#define F first
#define S second
#define sz(x) int(x.size())
#define pb push_back
#define N 100005
#define MOD ll(998244353)
using namespace std;
typedef long long ll;
typedef long double ld;
int n, k;
ld calc(int ost, int v, int j)
{
ld ans = 0;
while (n - ost >= v && j + 1 < k)
{
ost += v;
ans += ld(v) / ld(ost);
j++;
}
if (n - ost != 0) ans += ld(n - ost) / ld(n);
return ans;
}
int main()
{
ios_base::sync_with_stdio(0); istream::sync_with_stdio(0); cin.tie(0); cout.tie(0);
cin >> n >> k;
ld ans = 0;
int sm = 0, v = 1, j = 0;
while (sm < n && j < k)
{
ld sum = calc(sm, v, j);
ld nsum = calc(sm, v + 1, j);
if (sum >= nsum) {sm += v; if (j + 1 != k) ans += ld(v) / ld(sm); j++; if (j == k) ans += sum; continue;}
v++;
}
cout << setprecision(9) << fixed;
cout << ans << endl;
}
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