結果

問題 No.2262 Fractions
ユーザー とりゐとりゐ
提出日時 2023-03-09 11:05:06
言語 PyPy3
(7.3.15)
結果
AC  
実行時間 1,007 ms / 2,000 ms
コード長 5,233 bytes
コンパイル時間 421 ms
コンパイル使用メモリ 82,248 KB
実行使用メモリ 139,844 KB
最終ジャッジ日時 2024-11-27 02:00:15
合計ジャッジ時間 30,203 ms
ジャッジサーバーID
（参考情報） 		judge4 / judge3
このコードへのチャレンジ
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ファイルパターン 結果
sample AC * 1
other AC * 45
権限があれば一括ダウンロードができます

ソースコード

diff # 

from math import gcd


class Fraction:
    def __init__(self, num, den=1):
        if type(num) == float or type(num) == str:
            assert den == 1
            if type(num) == float:
                S = str("{:.10f}".format(num))
            else:
                S = num
            N = len(S)
            point = -1
            for i in range(N):
                if S[i] == ".":
                    point = i
            if point != -1:
                F = Fraction(int(S[:point] + S[point + 1 :]), 10 ** (N - 1 - point))
            else:
                F = Fraction(int(S), 1)
            self.num = F.num
            self.den = F.den
        elif type(num) == type(den) == int:
            assert den != 0
            """
            inf = 10**9
            if den == 0:
                if num > 0:
                    self.num = inf
                    self.den = 1
                elif num < 0:
                    self.num = -inf
                    self.den = 1
                else:
                    raise Exception
                return
            """
            den, num = max((den, num), (-den, -num))
            g = gcd(den, num)
            self.num = num // g
            self.den = den // g
        else:
            raise Exception

    def __str__(self):
        return str(self.num) + "/" + str(self.den)

    def __pos__(self):
        return self

    def __neg__(self):
        num, den = self.num, self.den
        return Fraction(-num, den)

    def __add__(self, other):
        if type(other) != Fraction:
            other = Fraction(other)
        num1, den1 = self.num, self.den
        num2, den2 = other.num, other.den
        return Fraction(num1 * den2 + num2 * den1, den1 * den2)

    def __sub__(self, other):
        if type(other) != Fraction:
            other = Fraction(other)
        num1, den1 = self.num, self.den
        num2, den2 = other.num, other.den
        return Fraction(num1 * den2 - num2 * den1, den1 * den2)

    def __mul__(self, other):
        if type(other) != Fraction:
            other = Fraction(other)
        num1, den1 = self.num, self.den
        num2, den2 = other.num, other.den
        return Fraction(num1 * num2, den1 * den2)

    def __truediv__(self, other):
        if type(other) != Fraction:
            other = Fraction(other)
        num1, den1 = self.num, self.den
        num2, den2 = other.num, other.den
        return Fraction(num1 * den2, num2 * den1)

    def __pow__(self, x):
        assert type(x) == int
        num, den = self.num, self.den
        if x >= 0:
            return Fraction(num**x, den**x)
        else:
            return Fraction(den ** (-x), num ** (-x))

    __radd__ = __add__

    def __rsub__(self, other):
        if type(other) != Fraction:
            other = Fraction(other)
        num1, den1 = other.num, other.den
        num2, den2 = self.num, self.den
        return Fraction(num1 * den2 - num2 * den1, den1 * den2)

    __rmul__ = __mul__

    def __rtruediv__(self, other):
        if type(other) != Fraction:
            other = Fraction(other)
        num1, den1 = other.num, other.den
        num2, den2 = self.num, self.den
        return Fraction(num1 * den2, num2 * den1)

    def __eq__(self, other):
        if type(other) != Fraction:
            other = Fraction(other)
        num1, den1 = self.num, self.den
        num2, den2 = other.num, other.den
        return num1 == num2 and den1 == den2

    def __lt__(self, other):
        if type(other) != Fraction:
            other = Fraction(other)
        num1, den1 = self.num, self.den
        num2, den2 = other.num, other.den
        return num1 * den2 < num2 * den1

    def __le__(self, other):
        if type(other) != Fraction:
            other = Fraction(other)
        num1, den1 = self.num, self.den
        num2, den2 = other.num, other.den
        return num1 * den2 <= num2 * den1

    def __gt__(self, other):
        if type(other) != Fraction:
            other = Fraction(other)
        num1, den1 = self.num, self.den
        num2, den2 = other.num, other.den
        return num1 * den2 > num2 * den1

    def __ge__(self, other):
        if type(other) != Fraction:
            other = Fraction(other)
        num1, den1 = self.num, self.den
        num2, den2 = other.num, other.den
        return num1 * den2 >= num2 * den1
    
    def floor(self):
      return self.num//self.den

from sys import stdin
input=lambda :stdin.readline()[:-1]

def calc(n,a):
  dp=[0]*(n+1)
  for i in range(1,n+1):
    s=(a*i)//n
    dp[i]+=s
    if dp[i]==0:
      continue
    for j in range(2*i,n+1,i):
      dp[j]-=dp[i]
  return sum(dp)

def solve():
  n,k=map(int,input().split())
  c=calc(n,n-1)
  if k==c+1:
    print('1/1')
    return
  if k<=c:
    rev=False
  elif k<=2*c+1:
    rev=True
    k=2*c+2-k
  else:
    print(-1)
    return

  ng,ok=n,0
  while abs(ok-ng)>1:
    mid=(ok+ng)//2
    if calc(n,mid)<=k:
      ok=mid
    else:
      ng=mid

  k-=calc(n,ok)
  fracs=[]

  for p in range(1,n+1):
    q=(ok*p+n-1)//n
    if q*n<(ok+1)*p:
      if gcd(p,q)==1:
        fracs.append(Fraction(q,p))

  fracs.sort()
  if rev:
    print(1/fracs[k])
  else:
    print(fracs[k])

for _ in range(int(input())):
  solve()
0