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A_Chores.cpp
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A_Chores.cpp
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#include "bits/stdc++.h"
using namespace std;
//#define int long long
#define FAST ios::sync_with_stdio(0),cin.tie(0),cout.tie(0);
#define size(x) (int)x.size()
#define all(x) x.begin(),x.end()
#define ln '\n'
#define __ ' '
#define LL long long
#define LD long double
#define pii pair<int,int>
const int INF = 1e9;
const int N = 1e6;
const int X = 2e6;
int n, p;
int spf[X+2];
int occ[X+2];
inline int _power(const LL &x, const LL &n){if(n==0)return 1;int y=_power(x, n>>1);y=y*y;return (n&1)?y*x:y;}
void contrib(int x, int add){
while(x > 1){
int pr = spf[x];
occ[pr] += add;
x /= pr;
}
}
LD f(int x){
memset(occ, 0, sizeof(occ));
contrib(x, 1);
for(int i=1; i<=n; ++i){
contrib(i, 1);
}
for(int i=1; i<=p-1; ++i){
contrib(i, -1);
}
for(int i=1; i<=n-(p-1); ++i){
contrib(i, -1);
}
for(int i=1; i<=n+x; ++i){
contrib(i, -1);
}
for(int i=1; i<=p; ++i){
contrib(i, 1);
}
for(int i=1; i<=n+x-p; ++i){
contrib(i, 1);
}
vector<int> pos, neg;
for(int key=1; key<=X; ++key){
int val = occ[key];
if(val > 0){
pos.emplace_back(_power(key, val));
}
if(val < 0){
neg.emplace_back(_power(key, -val));
}
}
LD tans = 1.0L;
while(!empty(pos) || !empty(neg)){
if(!empty(pos)){
tans *= pos.back();
pos.pop_back();
}
if(!empty(neg)){
tans /= neg.back();
neg.pop_back();
}
}
return tans;
}
int main(){ FAST
for(int i=1; i<=X; ++i){
spf[i] = i;
}
for(int i=2; i<=X; ++i) if(spf[i] == i){
for(int j=i+i; j<=X; j+=i){
spf[j] = min(spf[j], i);
}
}
cin >> n >> p;
LD ans = f(1);
LD curAns = f(1);
for(int x=2; x<=n; ++x){
curAns *= x;
curAns /= x-1;
curAns /= n+x;
curAns *= n+x-p;
ans = max(ans, curAns);
}
cout << fixed << setprecision(6) << ans << ln;
}