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>
#define in(x) freopen(x,"r",stdin)
#define out(x) freopen(x,"w",stdout)
#define F first
#define S second
#define pb push_back
#define M ll(998244353)
#define inf ll(2e9+7)
#define N ll(100500)
#define sz(x) x.size()
//#pragma GCC optimize("unroll-loops")
//#pragma GCC optimize("O3")
//#pragma GCC optimize("Ofast")
#define el '\n'
using namespace std;
typedef unsigned long long ull;
typedef long long ll;
typedef long double ld;
//#include <ext/pb_ds/assoc_container.hpp>
//#include <ext/pb_ds/tree_policy.hpp>
//using namespace __gnu_pbds;
//typedef tree <ll, null_type, less_equal <ll>, rb_tree_tag, tree_order_statistics_node_update> os;
ld f[N], b[N];
ll n, m, i, j, kol, sz, num[N], pr, K;
ld cht[N], k[N];
void AddInCHT(int i)
{
ld x;
while (1)
{
pr = num[sz];
x = (b[pr] - b[i]) / (k[i] - k[pr]);
// cerr << x << el;
if (x - cht[sz] > 1e-18) break;
sz--;
}
sz++;
cht[sz] = x;
num[sz] = i;
}
int ch(ld X)
{
sz = 1;
cht[sz] = -1e18;
num[sz] = n;
b[n] = 0;
f[n] = 0;
k[n] = 1.0 / ld(n);
for (i = n - 1; i >= 0; i--)
{
int l = 1;
int r = sz;
while (l < r)
{
int md = (l + r + 1) >> 1;
ld x = cht[md];
if (x + ld(i) < 1e-18) l = md;
else r = md - 1;
}
K = num[l];
f[i] = f[K] + 1;
b[i] = b[K] + 1 - ld(i) * k[K] + X;
k[i] = ld(1) / ld(i);
AddInCHT(i);
}
return f[0];
}
int main()
{
// in("input.txt");
// out("output.txt");
ios_base::sync_with_stdio(false);
iostream::sync_with_stdio(false);
cin.tie(NULL);
cin >> n >> m;
ld l = 0;
ld r = 1e12;
while (r - l > 1e-13)
{
ld md = (l + r) * 0.5;
if (ch(-md) > m) l = md + 1e-13;
else r = md;
}
ch(-l);
cout << setprecision(9) << fixed << b[0] + l * ld(m);
}
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