import std.conv, std.functional, std.range, std.stdio, std.string; import std.algorithm, std.array, std.bigint, std.bitmanip, std.complex, std.container, std.math, std.mathspecial, std.numeric, std.regex, std.typecons; import core.bitop; class EOFException : Throwable { this() { super("EOF"); } } string[] tokens; string readToken() { for (; tokens.empty; ) { if (stdin.eof) { throw new EOFException; } tokens = readln.split; } auto token = tokens.front; tokens.popFront; return token; } int readInt() { return readToken.to!int; } long readLong() { return readToken.to!long; } real readReal() { return readToken.to!real; } bool chmin(T)(ref T t, in T f) { if (t > f) { t = f; return true; } else { return false; } } bool chmax(T)(ref T t, in T f) { if (t < f) { t = f; return true; } else { return false; } } int binarySearch(alias pred, T)(in T[] as) { int lo = -1, hi = cast(int)(as.length); for (; lo + 1 < hi; ) { const mid = (lo + hi) >> 1; (unaryFun!pred(as[mid]) ? hi : lo) = mid; } return hi; } int lowerBound(T)(in T[] as, T val) { return as.binarySearch!(a => (a >= val)); } int upperBound(T)(in T[] as, T val) { return as.binarySearch!(a => (a > val)); } enum LIM = 3 * 10^^5 + 10; int[] lpf, moe; // 0 < p/q < 1, p/q <= t/N^2 long calc(long N, long t) { auto fs = new long[N + 1]; foreach (q; 1 .. N + 1) { fs[q] = q * t / (N*N); chmin(fs[q], q - 1); } foreach (q; 1 .. N + 1) { fs[q] += fs[q - 1]; } long ret; foreach (d; 1 .. N + 1) { if (moe[d] < 0) ret -= fs[N / d]; if (moe[d] > 0) ret += fs[N / d]; } return ret; } alias Frac = Tuple!(long, "p", long, "q"); Frac solve(long N, long K) { long lo = 0, hi = N*N; for (; lo + 1 < hi; ) { const mid = (lo + hi) / 2; ((calc(N, mid) >= K) ? hi : lo) = mid; } foreach (q; 1 .. N + 1) { const p = q * hi / (N*N); if (lo * q < p * (N*N)) { return Frac(p, q); } } assert(false); } void main() { lpf = iota(LIM).array; moe = new int[LIM]; moe[1 .. $] = 1; foreach (p; 2 .. LIM) if (lpf[p] == p) { for (int n = p; n < LIM; n += p) { chmin(lpf[n], p); moe[n] = -moe[n]; if (n / p % p == 0) moe[n] = 0; } } try { for (; ; ) { const numCases = readInt; foreach (caseId; 0 .. numCases) { const N = readLong; const K = readLong; Frac ans; const res = calc(N, N*N); if (K <= res) { ans = solve(N, K); } else if (K == res + 1) { ans = Frac(1, 1); } else if (K <= res + 1 + res) { ans = solve(N, (res + 1 + res) + 1 - K); swap(ans.p, ans.q); } if (ans.q) { writefln("%s/%s", ans.p, ans.q); } else { writeln(-1); } } } } catch (EOFException e) { } }