結果

問題 No.3038 シャッフルの再現
ユーザー gew1fw
提出日時 2025-06-12 15:29:58
言語 PyPy3
(7.3.15)
結果
RE  
実行時間 -
コード長 3,316 bytes
コンパイル時間 173 ms
コンパイル使用メモリ 82,964 KB
実行使用メモリ 70,600 KB
最終ジャッジ日時 2025-06-12 15:30:03
合計ジャッジ時間 2,609 ms
ジャッジサーバーID
（参考情報） 		judge2 / judge1
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ファイルパターン 結果
sample RE * 1
other RE * 21
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 # 

import math
import random

MOD = 10**9 + 7

def is_prime(n):
    if n < 2:
        return False
    for p in [2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37]:
        if n % p == 0:
            return n == p
    d = n - 1
    s = 0
    while d % 2 == 0:
        d //= 2
        s += 1
    for a in [2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37]:
        if a >= n:
            continue
        x = pow(a, d, n)
        if x == 1 or x == n - 1:
            continue
        for _ in range(s - 1):
            x = pow(x, 2, n)
            if x == n - 1:
                break
        else:
            return False
    return True

def pollards_rho(n):
    if n % 2 == 0:
        return 2
    if n % 3 == 0:
        return 3
    if n % 5 == 0:
        return 5
    while True:
        c = random.randint(1, n - 1)
        f = lambda x: (pow(x, 2, n) + c) % n
        x, y, d = 2, 2, 1
        while d == 1:
            x = f(x)
            y = f(f(y))
            d = math.gcd(abs(x - y), n)
        if d != n:
            return d

def factor(n):
    factors = []
    def _factor(n):
        if n == 1:
            return
        if is_prime(n):
            factors.append(n)
            return
        d = pollards_rho(n)
        _factor(d)
        _factor(n // d)
    _factor(n)
    return factors

def factorize(n):
    if n == 0:
        return {}
    factors = factor(n)
    res = {}
    for p in factors:
        res[p] = res.get(p, 0) + 1
    return res

def generate_divisors(factors):
    divisors = [1]
    for prime, exp in factors.items():
        temp = []
        for e in range(exp + 1):
            prime_power = prime ** e
            for d in divisors:
                temp.append(d * prime_power)
        divisors = temp
    return divisors

def fib_mod(n, mod):
    if mod == 1:
        return 0
    if n == 0:
        return 0
    a, b = 0, 1
    for _ in range(n):
        a, b = b, (a + b) % mod
    return a

def compute_pisano_period(p):
    if p == 2:
        return 3
    if p == 5:
        return 20
    mod = p
    remainder = p % 5
    if remainder == 1 or remainder == 4:
        d = p - 1
    else:
        d = 2 * (p + 1)
    if d == 0:
        return 0
    factors = factorize(d)
    divisors = generate_divisors(factors)
    divisors = list(set(divisors))
    divisors.sort()
    for m in divisors:
        if m == 0:
            continue
        fm = fib_mod(m, mod)
        fm1 = fib_mod(m + 1, mod)
        if fm == 0 and fm1 == 1:
            return m
    return d

def lcm(a, b):
    return a * b // math.gcd(a, b)

def main():
    import sys
    input = sys.stdin.read
    data = input().split()
    idx = 0
    n = int(data[idx])
    idx += 1
    primes = []
    for _ in range(n):
        p = int(data[idx])
        k = int(data[idx + 1])
        primes.append((p, k))
        idx += 2
    pisano_periods = []
    for p, k in primes:
        if p == 2:
            pi_p = 3
        elif p == 5:
            pi_p = 20
        else:
            pi_p = compute_pisano_period(p)
        if k == 1:
            pi_pk = pi_p
        else:
            pi_pk = pi_p * (p ** (k - 1))
        pisano_periods.append(pi_pk)
    current_lcm = 1
    for period in pisano_periods:
        current_lcm = lcm(current_lcm, period)
    print(current_lcm % MOD)

if __name__ == "__main__":
    main()
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