結果

問題 No.2066 Simple Math !
ユーザー lif4635
提出日時 2025-06-08 19:56:45
言語 PyPy3
(7.3.15)
結果
AC  
実行時間 669 ms / 2,000 ms
コード長 3,505 bytes
コンパイル時間 492 ms
コンパイル使用メモリ 82,664 KB
実行使用メモリ 78,956 KB
最終ジャッジ日時 2025-06-08 19:57:02
合計ジャッジ時間 15,544 ms
ジャッジサーバーID
（参考情報） 		judge2 / 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 * 31
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 # 

# input
import sys
input = sys.stdin.readline
II = lambda : int(input())
MI = lambda : map(int, input().split())
LI = lambda : [int(a) for a in input().split()]
SI = lambda : input().rstrip()
LLI = lambda n : [[int(a) for a in input().split()] for _ in range(n)]
LSI = lambda n : [input().rstrip() for _ in range(n)]
MI_1 = lambda : map(lambda x:int(x)-1, input().split())
LI_1 = lambda : [int(a)-1 for a in input().split()]

def graph(n:int, m:int, dir:bool=False, index:int=-1) -> list[set[int]]:
    edge = [set() for i in range(n+1+index)]
    for _ in range(m):
        a,b = map(int, input().split())
        a += index
        b += index
        edge[a].add(b)
        if not dir:
            edge[b].add(a)
    return edge

def graph_w(n:int, m:int, dir:bool=False, index:int=-1) -> list[set[tuple]]:
    edge = [set() for i in range(n+1+index)]
    for _ in range(m):
        a,b,c = map(int, input().split())
        a += index
        b += index
        edge[a].add((b,c))
        if not dir:
            edge[b].add((a,c))
    return edge

mod = 998244353
inf = 1001001001001001001
ordalp = lambda s : ord(s)-65 if s.isupper() else ord(s)-97
ordallalp = lambda s : ord(s)-39 if s.isupper() else ord(s)-97
yes = lambda : print("Yes")
no = lambda : print("No")
yn = lambda flag : print("Yes" if flag else "No")
def acc(a:list[int]):
    sa = [0]*(len(a)+1)
    for i in range(len(a)):
        sa[i+1] = a[i] + sa[i]
    return sa

prinf = lambda ans : print(ans if ans < 1000001001001001001 else -1)
alplow = "abcdefghijklmnopqrstuvwxyz"
alpup = "ABCDEFGHIJKLMNOPQRSTUVWXYZ"
alpall = "abcdefghijklmnopqrstuvwxyzABCDEFGHIJKLMNOPQRSTUVWXYZ"
URDL = {'U':(-1,0), 'R':(0,1), 'D':(1,0), 'L':(0,-1)}
DIR_4 = [[-1,0],[0,1],[1,0],[0,-1]]
DIR_8 = [[-1,0],[-1,1],[0,1],[1,1],[1,0],[1,-1],[0,-1],[-1,-1]]
DIR_BISHOP = [[-1,1],[1,1],[1,-1],[-1,-1]]
prime60 = [2,3,5,7,11,13,17,19,23,29,31,37,41,43,47,53,59]
sys.set_int_max_str_digits(0)
sys.setrecursionlimit(10**6)
# import pypyjit
# pypyjit.set_param('max_unroll_recursion=-1')

from collections import defaultdict,deque
from heapq import heappop,heappush
from bisect import bisect_left,bisect_right
DD = defaultdict
BSL = bisect_left
BSR = bisect_right

from math import gcd

def floor_sum(n, m, a, b):
    """
    sum_{0 <= i <= n - 1} floor(a * i + b / m)
    """
    res = 0
    while n:
        if a < 0 or m <= a:
            k, a = divmod(a, m)
            res += n*(n-1) * k >> 1
        if b < 0 or m <= b:
            k, b = divmod(b, m)
            res += n * k
        n, b = divmod(a*n+b, m)
        a, m = m, a
    return res

def solve(p, q, k):
    g = gcd(p, q)
    
    p //= g
    q //= g
    
    # p * q以上全部作れる
    
    ng = 0
    ok = p * q - 1
    r = floor_sum(q, q, -p, ok + q) - 1
    if r <= k:
        return (p * q - 1 + k - r) * g
    
    while abs(ok - ng) > 1:
        m = ok + ng >> 1
        s = floor_sum((m + q) // p + 1, q, -p, m + q) - 1
        if s >= k:
            ok = m
        else:
            ng = m
    return ok * g

def solve_naive(p, q, k):
    ok = set()
    for x in range(k + 1):
        for y in range(k + 1):
            ok.add(p * x + q * y)
    ok = sorted(ok)
    return ok[k]

t = II()
for i in range(t):
    p, q, k = MI()
    r = solve(p, q, k)
    
    print(r)
    
# from random import randint

# while True:
#     p, q, k = randint(1, 5), randint(1, 5), randint(1, 30)
#     r = solve(p, q, k)
#     r2 = solve_naive(p, q, k)
#     print(p, q, k, r, r2)
#     assert r == r2
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