#include #include using namespace std; using ll = long long; #define rep(i, s, t) for (int i = (int)(s); i < (int)(t); ++i) #define revrep(i, t, s) for (int i = (int)(t)-1; i >= (int)(s); --i) #define all(x) begin(x), end(x) template bool chmax(T& a, const T& b) { return a < b ? (a = b, 1) : 0; } template bool chmin(T& a, const T& b) { return a > b ? (a = b, 1) : 0; } template std::vector> quotient_ranges(T n) { std::vector> ret; T i = 1; while (i <= n) { T q = n / i; T j = n / q + 1; ret.emplace_back(i, j); i = j; } return ret; } template std::pair, std::vector> totient_summatory_table( long long n) { if (n == 0) return {{0}, {0}}; const int b = std::min(n, (long long)1e4); std::vector small(n / b + 1), large(b + 1); std::vector totient(n / b + 1); std::iota(totient.begin(), totient.end(), 0); for (int i = 2; i <= n / b; ++i) { if (totient[i] != i) continue; for (int j = i; j <= n / b; j += i) { totient[j] = totient[j] / i * (i - 1); } } for (int i = 0; i < n / b; ++i) small[i + 1] = small[i] + totient[i + 1]; for (int i = 1; i <= b; ++i) { mint k = n / i; large[i] = k * (k + 1) / 2; } for (long long i = b; i >= 1; --i) { for (long long l = 2; l <= n / i;) { long long q = n / (i * l), r = n / (i * q) + 1; large[i] -= (i * l <= b ? large[i * l] : small[n / (i * l)]) * (r - l); l = r; } } return {small, large}; } std::pair, std::vector> mertens_table(long long n) { if (n == 0) return {{0}, {0}}; const int b = 1e4; std::vector small(n / b + 1, 1), large(b + 1, 1); small[0] = large[0] = 0; std::vector prime(n / b + 1, true); for (int i = 2; i <= n / b; ++i) { if (!prime[i]) continue; for (int j = i; j <= n / b; j += i) { if (j > i) prime[j] = false; if ((j / i) % i == 0) small[j] = 0; else small[j] *= -1; } } for (int i = 1; i < n / b; ++i) small[i + 1] += small[i]; for (long long i = b; i >= 1; --i) { for (long long l = 2; l <= n / i;) { long long q = n / (i * l), r = n / (i * q) + 1; large[i] -= (i * l <= b ? large[i * l] : small[n / (i * l)]) * (r - l); l = r; } } return {small, large}; } using i128 = __int128_t; i128 floor_sum(i128 n, i128 m, i128 a, i128 b) { i128 sum = 0; if (a >= m) { sum += (a / m) * n * (n - 1) / 2; a %= m; } if (b >= m) { sum += (b / m) * n; b %= m; } i128 y = (a * n + b) / m; if (y == 0) return sum; i128 x = (m * y - b + a - 1) / a; sum += (n - x) * y + floor_sum(y, a, m, a * x - m * y + b); return sum; } std::vector moebius_table(int n) { std::vector prime(n + 1, true); std::vector ret(n + 1, 1); for (int i = 2; i <= n; ++i) { if (!prime[i]) continue; for (int j = i; j <= n; j += i) { if (j > i) prime[j] = false; if ((j / i) % i == 0) ret[j] = 0; else ret[j] *= -1; } } return ret; } int main() { ios_base::sync_with_stdio(false); cin.tie(nullptr); cout << fixed << setprecision(15); int N; ll K; cin >> N >> K; ll total = totient_summatory_table(N).second[1]; if (K >= 2 * total) { cout << -1 << endl; return 0; } bool flip = false; if (K > total) { K = 2 * total - K; flip = true; } auto qr = quotient_ranges(N); vector small, large; tie(small, large) = mertens_table(N); auto mertens = [&](ll n) -> ll { if (n < small.size()) return small[n]; return large[N / n]; }; const i128 D = 1e16 + 1; i128 lb = 0, ub = D + 1; while (ub - lb > 1) { ll m = (lb + ub) / 2; ll cnt = 0; for (auto [l, r] : qr) { cnt += (mertens(r - 1) - mertens(l - 1)) * floor_sum(N / l, D, m, m); } if (cnt < K) { lb = m; } else { ub = m; } } int lb2 = 0, ub2 = N + 1; while (ub2 - lb2 > 1) { int m2 = (lb2 + ub2) / 2; ll cnt = floor_sum(m2, D, ub, ub) - floor_sum(m2, D, ub - 1, ub - 1); if (cnt == 0) { lb2 = m2; } else { ub2 = m2; } } int d = ub2; int n = d * ub / D; if (flip) swap(d, n); cout << n << "/" << d << endl; }