#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; } 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}; } long long floor_sum(long long n, long long m, long long a, long long b) { long long sum = 0; if (a >= m) { sum += (a / m) * n * (n - 1) / 2; a %= m; } if (b >= m) { sum += (b / m) * n; b %= m; } long long y = (a * n + b) / m; if (y == 0) return sum; long long x = (m * y - b + a - 1) / a; sum += (n - x) * y + floor_sum(y, a, m, a * x - m * y + b); return sum; } template std::pair, std::pair> stern_brocot_tree_search(long long n, F cond) { long long a = 0, b = 1, c = 1, d = 0; while (true) { long long num = a + c, den = b + d; if (num > n || den > n) break; if (cond(num, den)) { long long k = 2; while ((num = a + c * k) <= n && (den = b + d * k) <= n && cond(num, den)) k *= 2; k /= 2; a = a + c * k; b = b + d * k; } else { long long k = 2; while ((num = a * k + c) <= n && (den = b * k + d) <= n && !cond(num, den)) k *= 2; k /= 2; c = a * k + c; d = b * k + d; } } return {{a, b}, {c, d}}; } int main() { ios_base::sync_with_stdio(false); cin.tie(nullptr); cout << fixed << setprecision(15); int N; ll K; cin >> N >> K; auto qr = quotient_ranges(N); vector small, large; tie(small, large) = mertens_table(N); auto mertens = [&](ll n) { if (n < (int)small.size()) return small[n]; return large[N / n]; }; auto count = [&](ll num, ll den) { ll cnt = 0; for (auto [l, r] : qr) { cnt += (mertens(r - 1) - mertens(l - 1)) * floor_sum(N / l, den, num, num); } return cnt; }; ll total = count(1, 1); if (K >= 2 * total) { cout << -1 << endl; return 0; } bool flip = false; if (K > total) { K = 2 * total - K; flip = true; } auto check = [&](ll num, ll den) { return count(num, den) < K; }; auto [num, den] = stern_brocot_tree_search(N, check).second; if (flip) swap(num, den); cout << num << "/" << den << endl; }