結果

問題 No.2262 Fractions
ユーザー chineristACchineristAC
提出日時 2023-04-07 23:34:33
言語 PyPy3
(7.3.15)
結果
AC  
実行時間 976 ms / 2,000 ms
コード長 5,545 bytes
コンパイル時間 378 ms
コンパイル使用メモリ 87,132 KB
実行使用メモリ 98,204 KB
最終ジャッジ日時 2023-08-18 00:33:55
合計ジャッジ時間 24,342 ms
ジャッジサーバーID
（参考情報） 		judge11 / judge12
このコードへのチャレンジ
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テストケース

テストケース表示
入力 結果 実行時間
実行使用メモリ
testcase_00 AC 249 ms
89,300 KB
testcase_01 AC 720 ms
94,820 KB
testcase_02 AC 713 ms
94,196 KB
testcase_03 AC 705 ms
96,152 KB
testcase_04 AC 945 ms
98,008 KB
testcase_05 AC 823 ms
95,992 KB
testcase_06 AC 733 ms
94,572 KB
testcase_07 AC 832 ms
97,920 KB
testcase_08 AC 832 ms
95,672 KB
testcase_09 AC 976 ms
98,204 KB
testcase_10 AC 758 ms
96,844 KB
testcase_11 AC 664 ms
93,036 KB
testcase_12 AC 666 ms
92,872 KB
testcase_13 AC 753 ms
94,616 KB
testcase_14 AC 686 ms
92,812 KB
testcase_15 AC 648 ms
93,448 KB
testcase_16 AC 212 ms
88,376 KB
testcase_17 AC 214 ms
89,004 KB
testcase_18 AC 214 ms
88,632 KB
testcase_19 AC 563 ms
95,048 KB
testcase_20 AC 478 ms
93,484 KB
testcase_21 AC 450 ms
92,656 KB
testcase_22 AC 454 ms
93,352 KB
testcase_23 AC 466 ms
91,968 KB
testcase_24 AC 272 ms
89,796 KB
testcase_25 AC 300 ms
89,768 KB
testcase_26 AC 362 ms
90,244 KB
testcase_27 AC 384 ms
91,000 KB
testcase_28 AC 371 ms
91,448 KB
testcase_29 AC 402 ms
91,032 KB
testcase_30 AC 304 ms
90,224 KB
testcase_31 AC 309 ms
89,996 KB
testcase_32 AC 342 ms
89,716 KB
testcase_33 AC 380 ms
90,928 KB
testcase_34 AC 297 ms
89,964 KB
testcase_35 AC 196 ms
88,784 KB
testcase_36 AC 188 ms
88,512 KB
testcase_37 AC 167 ms
87,080 KB
testcase_38 AC 166 ms
86,736 KB
testcase_39 AC 358 ms
91,560 KB
testcase_40 AC 418 ms
91,624 KB
testcase_41 AC 593 ms
94,308 KB
testcase_42 AC 483 ms
93,840 KB
testcase_43 AC 325 ms
90,988 KB
testcase_44 AC 361 ms
90,420 KB
testcase_45 AC 317 ms
89,908 KB
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ソースコード

diff # 

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)


        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)
0