#ifndef CLASS_POLYNOMIAL #define CLASS_POLYNOMIAL #include #include #include #include class polynomial { private: using type = double; const type epsilon = 1.0e-9; std::size_t sz; std::vector a; inline bool equivalent(type ra, type rb) const { return (epsilon <= ra - rb && ra - rb <= epsilon); } void discrete_fourier_transform(std::vector >& v, bool rev) { std::size_t n = v.size(); const type pi = acos(type(-1)); for (std::size_t i = 0, j = 1; j < n - 1; ++j) { for (std::size_t k = n >> 1; k > (i ^= k); k >>= 1); if (i > j) std::swap(v[i], v[j]); } for (std::size_t b = 1; b < n; b <<= 1) { std::complex wr = std::polar(type(1), (rev ? type(-1) : type(1)) * pi / b); for (std::size_t i = 0; i < n; i += 2 * b) { std::complex w = type(1); for (std::size_t j = 0; j < b; ++j) { std::complex v0 = v[i + j]; std::complex v1 = w * v[i + j + b]; v[i + j] = v0 + v1; v[i + j + b] = v0 - v1; w *= wr; } } } if (!rev) return; for (std::size_t i = 0; i < n; i++) v[i] /= n; } public: explicit polynomial() : sz(1), a(std::vector({ type() })) {}; explicit polynomial(std::size_t sz_) : sz(sz_), a(std::vector(sz_, type())) {}; explicit polynomial(std::vector a_) : sz(a_.size()), a(a_) {}; std::size_t size() { return sz; } std::size_t degree() { return sz - 1; } type operator[](std::size_t idx) const { return a[idx]; } type& operator[](std::size_t idx) { return a[idx]; } bool operator==(const polynomial& p) const { for (std::size_t i = 0; i < sz && i < p.sz; ++i) { if (!equivalent(i < sz ? a[i] : type(0), i < p.sz ? p.a[i] : type(0))) { return false; } } return true; } bool operator!=(const polynomial& p) const { return !(operator==(p)); } polynomial& operator+=(const polynomial& p) { sz = std::max(sz, p.sz); a.resize(sz); for (std::size_t i = 0; i < sz; ++i) a[i] += p.a[i]; return (*this); } polynomial& operator-=(const polynomial& p) { sz = std::max(sz, p.sz); a.resize(sz); for (std::size_t i = 0; i < sz; ++i) a[i] -= p.a[i]; return (*this); } polynomial& operator*=(const polynomial& p) { std::size_t n = 2; while (n < sz * 2 || n < p.sz * 2) n <<= 1; std::vector > v(n), pv(n); for (std::size_t i = 0; i < sz; ++i) v[i] = a[i]; for (std::size_t i = 0; i < p.sz; ++i) pv[i] = p.a[i]; discrete_fourier_transform(v, false); discrete_fourier_transform(pv, false); for (std::size_t i = 0; i < n; ++i) v[i] *= pv[i]; discrete_fourier_transform(v, true); sz += p.sz - 1; a.resize(sz, type(0)); for (std::size_t i = 0; i < sz; ++i) a[i] = v[i].real(); return (*this); } polynomial operator+() const { return polynomial(*this); } polynomial operator-() const { return polynomial() - polynomial(*this); } polynomial operator+(const polynomial& p) const { return polynomial(*this) += p; } polynomial operator-(const polynomial& p) const { return polynomial(*this) -= p; } polynomial operator*(const polynomial& p) const { return polynomial(*this) *= p; } }; #endif #include #include #include using namespace std; int main() { cin.tie(0); ios_base::sync_with_stdio(false); long long N, L, R; cin >> N >> L >> R; L = max(L, N); R = min(R, 6 * N); cout.precision(15); if (N > 3000) { double mean = 3.5 * N; double stdev = sqrt(35.0 / 12.0 * N); double probl = erf(((L - 0.5) - mean) / (sqrt(2.0) * stdev)) / 2; double probr = erf(((R + 0.5) - mean) / (sqrt(2.0) * stdev)) / 2; cout << probr - probl << endl; } else { polynomial b(7); for (int i = 1; i <= 6; ++i) b[i] = 1.0 / 6.0; polynomial ans(1); ans[0] = 1; while (N > 0) { if (N & 1) ans *= b; b *= b; N >>= 1; } double prob = 0.0; for (long long i = L; i <= R; ++i) { prob += ans[i]; } cout << prob << endl; } return 0; }