#include #define EPS 1e-9 #define INF 1070000000LL #define MOD 1000000007LL #define fir first #define foreach(it,X) for(auto it=(X).begin();it!=(X).end();it++) #define numa(x,a) for(auto x: a) #define ite iterator #define mp make_pair #define mt make_tuple #define rep(i,n) rep2(i,0,n) #define rep2(i,m,n) for(int i=m;i<(n);i++) #define pb push_back #define pf push_front #define sec second #define sz(x) ((int)(x).size()) #define ALL( c ) (c).begin(), (c).end() #define gcd(a,b) __gcd(a,b) #define mem(x,n) memset(x,n,sizeof(x)) #define endl "\n" using namespace std; template void deploy(std::ostream &os, const TUPLE &tuple){} template void deploy(std::ostream &os, const TUPLE &t){ os << (POS == 0 ? "" : ", ") << get(t); deploy(os, t); } template std::ostream& operator<<(std::ostream &os, std::pair &v){os << "(" << v.first << ", " << v.second << ")"; } template std::ostream& operator<<(std::ostream &os, std::vector &v){ int remain = v.size(); os << "{"; for(auto e: v) os << e << (--remain == 0 ? "}" : ", "); return os; } template std::ostream& operator<<(std::ostream &os, std::set &v){ int remain = v.size(); os << "{"; for(auto e: v) os << e << (--remain == 0 ? "}" : ", "); return os; } template std::ostream& operator<<(std::ostream &os, std::map &mp){ int remain = mp.size(); os << "{"; for(auto e: mp) os << "(" << e.first << " -> " << e.second << ")" << (--remain == 0 ? "}" : ", "); return os; } #define DEBUG1(var0) { std::cerr << (#var0) << "=" << (var0) << endl; } #define DEBUG2(var0, var1) { std::cerr << (#var0) << "=" << (var0) << ", ";DEBUG1(var1); } #define DEBUG3(var0, var1, var2) { std::cerr << (#var0) << "=" << (var0) << ", ";DEBUG2(var1,var2); } #define DEBUG4(var0, var1, var2, var3) { std::cerr << (#var0) << "=" << (var0) << ", ";DEBUG3(var1,var2,var3); } using ll = long long; int N,K; map tmp1; map tmp2; map tmp3; map tmp4; map res1; map res2; map taro; map jiro; vector > taro_c; vector > jiro_c; void count2(int n,int sum,bool flag){ if(n == 0){ if(flag){ tmp1[sum] += 1; }else{ tmp2[sum] += 1; } }else{ for(int i = 1;i <= 6;i++){ count2(n-1,sum+i,flag); } } return; } void count3(int k,int sum,int tm,bool flag){ if(k == 0){ if(flag){ tmp3[sum] += tm; }else{ tmp4[sum] += tm; } }else{ for(int i = 4;i <= 6;i++){ count3(k-1,sum+i,tm*2,flag); } } } void count(int n,int k,bool is_taro){ tmp1.clear();tmp2.clear();tmp3.clear();tmp4.clear(); count2((n-k)/2,0,true); count2((n-k+1)/2,0,false); count3(k/2,0,1,true); count3((k+1)/2,0,1,false); res1.clear();res2.clear(); numa(c1,tmp1){ numa(c2,tmp2){ res1[c1.fir+c2.fir] += c1.sec*c2.sec; } } numa(c3,tmp3){ numa(c4,tmp4){ res2[c3.fir+c4.fir] += c3.sec*c4.sec; } } numa(r1,res1){ numa(r2,res2){ if(is_taro){ taro[r1.fir+r2.fir] += r1.sec*r2.sec; }else{ jiro[r1.fir+r2.fir] += r1.sec*r2.sec; } } } return; } int main(){ cin.tie(0); ios_base::sync_with_stdio(0); cin >> N >> K; count(N,0,true); count(N,K,false); numa(x,taro){ taro_c.pb(x); } numa(x,jiro){ jiro_c.pb(x); } { int sums = 0; for(int i = sz(jiro_c)-1;i>=0;i--){ sums += jiro_c[i].sec; jiro_c[i].sec = sums; } } ll ans_child = 0; rep(i,sz(taro_c)){ auto it = upper_bound(ALL(jiro_c),taro_c[i],[](pair a,pair b){return a.fir < b.fir;}); if(it != jiro_c.end()){ ans_child += (ll) taro_c[i].sec * (ll) it->sec; } } long double ans = ans_child; rep(i,2*N){ ans /= 6; } cout << fixed << setprecision(10) << ans << endl; return 0; }