#include using namespace std; namespace arithmetic { template class Addition { public: template T operator+(const V& v) const { T res(static_cast(*this)); return res += static_cast(v); } }; template class Subtraction { public: template T operator-(const V& v) const { T res(static_cast(*this)); return res -= static_cast(v); } }; template class Multiplication { public: template T operator*(const V& v) const { T res(static_cast(*this)); return res *= static_cast(v); } }; template class Division { public: template T operator/(const V& v) const { T res(static_cast(*this)); return res /= static_cast(v); } }; template class Modulus { public: template T operator%(const V& v) const { T res(static_cast(*this)); return res %= static_cast(v); } }; } template class IndivisibleArithmetic : public arithmetic::Addition, public arithmetic::Subtraction, public arithmetic::Multiplication {}; template class Arithmetic : public IndivisibleArithmetic, public arithmetic::Division {}; template class Vector : public arithmetic::Addition>, public arithmetic::Subtraction> { protected: vector val; public: Vector(int n) : val(n, 0) {} T& operator[](int n) { return val[n]; } Vector operator+=(const Vector& v) { for (int i = 0; i < size(); ++i) val[i] += v[i]; return *this; } Vector operator-=(const Vector& v) { for (int i = 0; i < size(); ++i) val[i] -= v[i]; return *this; } T operator*(const Vector& v) const { return inner_product(val.begin(), val.end(), const_cast(v).begin(), T(0)); } int size() const { return val.size(); } typename vector::const_iterator begin() const { return val.begin(); } typename vector::const_iterator end() const { return val.end(); } }; template class Matrix : public arithmetic::Addition>, public arithmetic::Subtraction> { protected: vector> val; public: Matrix(int n, int m) : val(n, Vector(m)) {} Vector& operator[](int n) { return val[n]; } Matrix operator+=(const Matrix& m) { for (int i = 0; i < (int)val.size(); ++i) val[i] += m[i]; return *this; } Matrix operator-=(const Matrix& m) { for (int i = 0; i < (int)val.size(); ++i) val[i] -= m[i]; return *this; } Matrix operator*=(const Matrix& _m) { Matrix &m = const_cast(_m); Matrix res(size(), m[0].size()); for (int i = 0; i < size(); ++i) { for (int j = 0; j < m.size(); ++j) { for (int k = 0; k < m[0].size(); ++k) { res[i][k] += val[i][j] * m[j][k]; } } } return *this = res; } Matrix operator*(const Matrix& m) const { Matrix res = *this; return res *= m; } Vector operator*(const Vector& v) { Vector res(size()); for (int i = 0; i < size(); ++i) res[i] += val[i] * v; return res; } int size() const { return val.size(); } }; template class SquareMatrix : public Matrix, public arithmetic::Division> { public: SquareMatrix(int n) : Matrix(n, n) {} SquareMatrix(const Matrix& m) : Matrix(m) {} SquareMatrix operator/=(const SquareMatrix& m) { return *this *= m.inverse(); } SquareMatrix identity() const { SquareMatrix res(this->size()); for (int i = 0; i < this->size(); ++i) res[i][i] = 1; return res; } SquareMatrix inverse() const { int n = this->size(); SquareMatrix mat = *this; SquareMatrix inv = identity(); for (int i = 0; i < n; ++i) { int p = i; for (int j = i + 1; j < n; ++j) { if (abs(mat[j][i]) > abs(mat[p][i])) p = j; } swap(mat[i], mat[p]); swap(inv[i], inv[p]); for (int j = i + 1; j < n; ++j) mat[i][j] /= mat[i][i]; for (int j = 0; j < n; ++j) inv[i][j] /= mat[i][i]; mat[i][i] = 1; for (int j = 0; j < n; ++j) { if (i == j) continue; T a = mat[j][i]; for (int k = 0; k < n; ++k) { mat[j][k] -= a * mat[i][k]; inv[j][k] -= a * inv[i][k]; } } } return inv; } }; template T pow(T& m, long long n) { if (n == 0) { return m.identity(); } else if (n < 0) { return m.identity() / pow(m, -n); } T mm = pow(m, n / 2); mm *= mm; if (n % 2) mm *= m; return mm; } int main() { int n, k; cin >> n >> k; const int mx = 6 * n; SquareMatrix m1(mx + 1), m2(mx + 1); for (int i = 0; i < mx; ++i) { for (int j = 1; j <= 6; ++j) { if (i + j <= mx) m1[i + j][i] = 1.0 / 6; } for (int j = 4; j <= 6; ++j) { if (i + j <= mx) m2[i + j][i] = 2.0 / 6; } } Vector v(mx + 1); v[0] = 1; auto taro = (Matrix)pow(m1, n - k) * (Matrix)pow(m2, k) * v; auto jiro = pow(m1, n) * v; double res = 0; for (int i = 0; i <= mx; ++i) { for (int j = 0; j < i; ++j) res += taro[i] * jiro[j]; } cout << fixed << setprecision(15) << res << endl; }