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 20:58:05
言語 PyPy3
(7.3.15)
結果
RE  
実行時間 -
コード長 3,767 bytes
コンパイル時間 146 ms
コンパイル使用メモリ 82,480 KB
実行使用メモリ 70,564 KB
最終ジャッジ日時 2025-06-12 21:01:51
合計ジャッジ時間 2,436 ms
ジャッジサーバーID
（参考情報） 		judge3 / judge2
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 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 sys
import random
from math import gcd
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 = 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)
    factors.sort()
    return factors

def get_prime_factors(n):
    if n == 1:
        return []
    factors = factor(n)
    result = []
    prev = factors[0]
    count = 1
    for p in factors[1:]:
        if p == prev:
            count +=1
        else:
            result.append( (prev, count) )
            prev = p
            count =1
    result.append( (prev, count) )
    return result

def generate_divisors(factors):
    divisors = [1]
    for (p, exp) in factors:
        temp = []
        for d in divisors:
            current = d
            for e in range(1, exp+1):
                current *= p
                temp.append(current)
        divisors += temp
    divisors = list(set(divisors))
    divisors.sort()
    return divisors

def legendre_symbol(a, p):
    ls = pow(a, (p-1)//2, p)
    if ls == p-1:
        return -1
    return ls

def fast_doubling(n, p):
    def fib_pair(n):
        if n == 0:
            return (0, 1)
        a, b = fib_pair(n >> 1)
        c = (a * (2 * b - a)) % p
        d = (a * a + b * b) % p
        if n & 1:
            return (d, (c + d) % p)
        else:
            return (c, d)
    return fib_pair(n)

def compute_pisano_period(p):
    if p == 2:
        return 3
    if p == 5:
        return 20
    res = legendre_symbol(5, p)
    if res == 1:
        D = p - 1
    else:
        D = 2 * (p + 1)
    if D == 0:
        return 1
    factors = get_prime_factors(D)
    divisors = generate_divisors(factors)
    for n in divisors:
        a, b = fast_doubling(n, p)
        if a == 0 and b == 1:
            return n
    return D

def compute_lcm(a, b):
    return a * b // gcd(a, b)

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

if __name__ == "__main__":
    main()
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