import sys,random,bisect from collections import deque,defaultdict from heapq import heapify,heappop,heappush from itertools import permutations from math import gcd,log input = lambda :sys.stdin.readline().rstrip() mi = lambda :map(int,input().split()) li = lambda :list(mi()) from collections import deque class Dinic: def __init__(self, N): self.N = N self.G = [[] for i in range(N)] def add_edge(self, fr, to, cap): forward = [to, cap, None] forward[2] = backward = [fr, 0, forward] self.G[fr].append(forward) self.G[to].append(backward) def add_multi_edge(self, v1, v2, cap1, cap2): edge1 = [v2, cap1, None] edge1[2] = edge2 = [v1, cap2, edge1] self.G[v1].append(edge1) self.G[v2].append(edge2) def bfs(self, s, t): self.level = level = [None]*self.N deq = deque([s]) level[s] = 0 G = self.G while deq: v = deq.popleft() lv = level[v] + 1 for w, cap, _ in G[v]: if cap and level[w] is None: level[w] = lv deq.append(w) return level[t] is not None def dfs(self, v, t, f): if v == t: return f level = self.level for e in self.it[v]: w, cap, rev = e if cap and level[v] < level[w]: d = self.dfs(w, t, min(f, cap)) if d: e[1] -= d rev[1] += d return d return 0 def flow(self, s, t): flow = 0 INF = 10**9 + 7 G = self.G while self.bfs(s, t): *self.it, = map(iter, self.G) f = INF while f: f = self.dfs(s, t, INF) flow += f return flow def floor_sum(n: int, m: int, a: int, b: int) -> int: ans = 0 if a >= m: ans += (n - 1) * n * (a // m) // 2 a %= m if b >= m: ans += n * (b // m) b %= m y_max = (a * n + b) // m x_max = y_max * m - b if y_max == 0: return ans ans += (n - (x_max + a - 1) // a) * y_max ans += floor_sum(y_max, a, m, (a - x_max % a) % a) return ans M = 3*10**5 + 1 mebius = [1] * (M+1) prime = [True] * (M+1) for p in range(2,M+1): if not prime[p]: continue for n in range(p,M+1,p): if n%(p*p) == 0: mebius[n] = 0 mebius[n] *= -1 prime[n] = False mebius_cum = [mebius[n] for n in range(M+1)] mebius[0] = 0 for n in range(1,M): mebius_cum[n+1] += mebius_cum[n] def solve(N,K): lower = (0,1) upper = (1,0) calc = 0 def cond(p,q): nonlocal calc calc += 1 #assert p <= N and q <= N """ ・qx<=py ・1 <= x,y <= N ・gcd(x,y)=1 をみたすx,yを数える gcd(x,y)がkの倍数とすると sum((N//k)-(qi)//p for i in range(1,(N//k)+1)) -> floor_sum +メビウス変換 """ res = 0 B = int(N**.5) for k in range(1,B+1): t = N//k tmp = 0 ok = -1 ng = t while ng-ok>1: mid = (ok+ng)//2 if (q*mid+q-1)//p <= t: ok = mid else: ng = mid tmp = t * ng - floor_sum(ng,p,q,q-1) res += tmp * mebius[k] for t in range(1,N//(B+1)+1): k_l = N//(t+1)+1 k_r = N//t tmp = 0 ok = -1 ng = t while ng-ok>1: mid = (ok+ng)//2 if (q*mid+q-1)//p <= t: ok = mid else: ng = mid tmp = t * ng - floor_sum(ng,p,q,q-1) res += tmp * (mebius_cum[k_r] - mebius_cum[k_l-1]) return res if cond(N,1) < K: print(-1) return while True: a,b = lower c,d = upper p,q = (a+c,b+d) if a+b >= N and c+d >= N: print(-1) return check = cond(p,q) if check < K: """ 右に潜る """ ok = 1 if d!=0: ng = min((N-b)//d,(N-a)//c) + 1 else: ng = (N-a)//c + 1 while ng-ok>1: mid = (ok+ng)//2 p,q = a+c*mid,b+d*mid xxx = cond(p,q) if xxx < K: ok = mid elif K < xxx: ng = mid else: p,q = a+c*mid,b+d*mid print("{}/{}".format(p,q)) return lower = (a+c*ok,b+d*ok) elif K < check: """ 左に潜る """ ok = 1 if a!=0: ng = min((N-d)//b,(N-c)//a) + 1 else: ng = (N-d)//b + 1 while ng-ok>1: mid = (ok+ng)//2 p,q = a*mid+c,b*mid+d if cond(p,q) > K: ok = mid else: ng = mid upper = (a*ok+c,b*ok+d) else: print("{}/{}".format(p,q)) return for _ in range(int(input())): N,K = mi() solve(N,K)