Runs

#include <cstdio>
#include <iostream>
#include <algorithm>
#include <vector>
#include <string>
#include <queue>
#include <map>
#include <set>
#include <cmath>
#include <sstream>
#include <stack>
#include <cassert>

#define pb push_back
#define mp make_pair
#define PI 3.1415926535897932384626433832795
#define sqr(x) (x)*(x)
#define forn(i, n) for(int i = 0; i < n; ++i)
#define ALL(x) x.begin(), x.end()
#define F first
#define S second
#define m0(x) memset(x,0,sizeof(x))
#define CC(x) cout << (x) << "\n"
#define pw(x) (1ull<<(x)).

using namespace std;
typedef long long ll;
typedef unsigned long long ull;
typedef long double ld;
typedef pair<int,int> pii;
const int INF = 2147483647;
const ll LLINF = 9223372036854775807LL;

ld d[550][550];

int main() {
  freopen("runs.in", "r", stdin);
  freopen("runs.out", "w", stdout);

  int n,r;
  cin >> n >> r;
  forn(i,550) forn(k,550) d[i][k]=0;
  d[1][1]=1;
  d[2][1]=1;
  for(int i=3; i<=n; i++) {
    for(int k=1; k<i; k++) {
      ld ch0 = d[i-1][k]*k;
      ld ch1=0, ch2=0;
      if (k>=2) ch1=d[i-1][k-1]*2;
      if (k>=3) ch2=d[i-1][k-2]*(i-k);
      if (ch2<0) ch2=0;
      d[i][k]=(ch0+ch1+ch2)/i;
    }
  }
  double ans = d[n][r];
  printf("%0.11lf\n", ans);
  return 0;
}