結果

問題 No.2 素因数ゲーム
コンテスト
ユーザー xpic
提出日時 2024-11-23 23:21:19
言語 PyPy3
(7.3.15)
結果
AC  
実行時間 59 ms / 5,000 ms
コード長 5,265 bytes
コンパイル時間 266 ms
コンパイル使用メモリ 81,920 KB
実行使用メモリ 55,424 KB
最終ジャッジ日時 2024-11-23 23:21:23
合計ジャッジ時間 2,753 ms
ジャッジサーバーID
（参考情報） 		judge1 / judge5
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ファイルパターン 結果
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 #
raw source code 

import os
import sys
from io import BytesIO, IOBase
from random import randint, randrange
from math import gcd

BUFSIZE = 1 << 15


class FastIO(IOBase):
    newlines = 0

    def __init__(self, file):
        self._fd = file.fileno()
        self.buffer = BytesIO()
        self.writable = "x" in file.mode or "r" not in file.mode
        self.write = self.buffer.write if self.writable else None

    def read(self):
        while True:
            b = os.read(self._fd, max(os.fstat(self._fd).st_size, BUFSIZE))
            if not b:
                break
            ptr = self.buffer.tell()
            self.buffer.seek(0, 2), self.buffer.write(b), self.buffer.seek(ptr)
        self.newlines = 0
        return self.buffer.read()

    def readline(self):
        while self.newlines == 0:
            b = os.read(self._fd, max(os.fstat(self._fd).st_size, BUFSIZE))
            self.newlines = b.count(b"\n") + (not b)
            ptr = self.buffer.tell()
            self.buffer.seek(0, 2), self.buffer.write(b), self.buffer.seek(ptr)
        self.newlines -= 1
        return self.buffer.readline()

    def flush(self):
        if self.writable:
            os.write(self._fd, self.buffer.getvalue())
            self.buffer.truncate(0), self.buffer.seek(0)


class IOWrapper(IOBase):
    def __init__(self, file):
        self.buffer = FastIO(file)
        self.flush = self.buffer.flush
        self.writable = self.buffer.writable
        self.write = lambda s: self.buffer.write(s.encode("ascii"))
        self.read = lambda: self.buffer.read().decode("ascii")
        self.readline = lambda: self.buffer.readline().decode("ascii")


def print(*args, **kwargs):
    """Prints the values to a stream, or to sys.stdout by default."""
    sep, file = kwargs.pop("sep", " "), kwargs.pop("file", sys.stdout)
    at_start = True
    for x in args:
        if not at_start:
            file.write(sep)
        file.write(str(x))
        at_start = False
    file.write(kwargs.pop("end", "\n"))
    if kwargs.pop("flush", False):
        file.flush()


def miller_rabin(n, bases):
    m, d, s = n - 1, n - 1, 0
    while d % 2 == 0:
        d >>= 1
        s += 1
    for base in bases:
        if n <= base:
            return True
        base = pow(base, d, n)
        if base == 1:
            continue
        r = 1
        while base != m:
            if r == s:
                return False
            base = base * base % n
            r += 1
    return True


def is_prime(n):
    if n <= 1:
        return False
    if n <= 3:
        return True
    if n & 1 == 0:
        return False
    if n < 4759123141:
        return miller_rabin(n, [2, 7, 61])
    if n < 18446744073709551615:
        return miller_rabin(n, [2, 325, 9375, 28178, 450775, 9780504, 1795265022])
    d = (n - 1) >> 1
    while d & 1 == 0:
        d >>= 1
    for _ in range(100):
        a = randint(1, n - 1)
        t = d
        y = pow(a, t, n)
        while t != n - 1 and y != 1 and y != n - 1:
            y = (y * y) % n
            t <<= 1
        if y != n - 1 and t & 1 == 0:
            return False
    return True


def find_prime_factor(n: int) -> int:
    b = n.bit_length() - 1
    b = (b >> 2) << 2
    m = (1 << (b >> 3)) << 1
    while True:
        c = randrange(1, n)
        f = lambda a: (pow(a, 2, n) + c) % n
        y = 0
        g = q = r = 1
        while g == 1:
            x = y
            for _ in range(r):
                y = f(y)
            k = 0
            while k < r and g == 1:
                ys = y
                for _ in range(min(m, r - k)):
                    y = f(y)
                    q = q * abs(x - y) % n
                g = gcd(q, n)
                k += m
            r <<= 1
        if g == n:
            g = 1
            y = ys
            while g == 1:
                y = f(y)
                g = gcd(abs(x - y), n)
        if g == n:
            continue
        if is_prime(g):
            return g
        elif is_prime(n // g):
            return n // g
        else:
            n = g


def factorize(n: int):
    res = []
    for p in range(2, 1000):
        if p * p > n:
            break
        if n % p:
            continue
        while n % p == 0:
            n //= p
            res.append(p)
    while not is_prime(n) and n > 1:
        p = find_prime_factor(n)
        while n % p == 0:
            n //= p
            res.append(p)
    if n > 1:
        res.append(n)
    return sorted(res)


def pe_factors(n: int):
    res = []
    e = 0
    while n % 2 == 0:
        n //= 2
        e += 1
    res.append((2, e))
    for p in range(3, 1000, 2):
        e = 0
        if p * p > n:
            break
        if n % p:
            continue
        while n % p == 0:
            n //= p
            e += 1
        res.append((p, e))
    while not is_prime(n) and n > 1:
        e = 0
        p = find_prime_factor(n)
        while n % p == 0:
            n //= p
            e += 1
        res.append((p, e))
    if n > 1:
        res.append((n, 1))
    return sorted(res)


sys.stdin, sys.stdout = IOWrapper(sys.stdin), IOWrapper(sys.stdout)
input = lambda: sys.stdin.readline().rstrip("\r\n")


N = int(input())
g = 0
for _, e in pe_factors(N):
    g ^= e
print("Bob" if g == 0 else "Alice")
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