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>
#include <time.h>
//#include <random>
#define sz(x) int(x.size())
#define in(x) freopen(x, "r", stdin)
#define out(x) freopen(x, "w", stdout)
#define N 100500
#define oo ll(1e16)
#define pii pair <int, int>
#define pll pair <ll, ll>
#define ft first
#define sd second
#define pb push_back
#define ppb pop_back
#define el '\n'
#define elf endl
#define base ll(1e9 + 7)
#define re return
#define nins 4294967295
using namespace std;
typedef long long ll;
typedef long double ld;
//mt19937 rnd(0);
int n, k;
ld f[2][N];
void solve(int cr, int l, int r, int opl, int opr) {
if (l > r)
return;
int md = (l + r) >> 1;
int op = -1;
for (int i = opl; i <= min(md, opr); i++) {
if (f[1 ^ cr][i] == -1)
continue;
if (f[cr ^ 1][i] + ld(md - i) / ld(md) > f[cr][md]) {
f[cr][md] = f[cr ^ 1][i] + ld(md - i) / ld(md);
op = i;
}
}
solve(cr, l, md - 1, opl, op);
solve(cr, md + 1, r, op, opr);
}
void solve() {
cin >> n >> k;
for (int i = 0; i <= n; i++)
f[1][i] = 1;
for (int i = 2; i <= k; i++) {
for (int j = 0; j <= n; j++)
f[i & 1][j] = -1;
solve(i & 1, 1, n, 1, n);
}
cout.precision(10); cout << fixed;
cout << f[k & 1][n];
}
int main() {
ios_base::sync_with_stdio(0); cin.tie(0); cout.tie(0);
#ifdef _LOCAL
in("input.txt");
int t = 1;
// cin >> t;
for (int i = 1; i <= t; i++) {
cout << "Test #" << i << elf;
clock_t start_time = clock();
solve();
cerr.precision(4); cerr << fixed;
cerr << elf;
cerr << "Time :: " << ld(clock() - start_time) / CLOCKS_PER_SEC << elf;
cout << elf;
}
#else
int t = 1;
// cin >> t;
while (t--) {
solve();
cout << el;
}
#endif
}
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