結果

問題 No.3038 シャッフルの再現
ユーザー lam6er
提出日時 2025-04-15 23:35:27
言語 PyPy3
(7.3.15)
結果
RE  
実行時間 -
コード長 3,449 bytes
コンパイル時間 198 ms
コンパイル使用メモリ 81,604 KB
実行使用メモリ 69,856 KB
最終ジャッジ日時 2025-04-15 23:36:31
合計ジャッジ時間 2,144 ms
ジャッジサーバーID
（参考情報） 		judge3 / 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 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[n] = factors.get(n, 0) + 1
            return
        d = pollards_rho(n)
        _factor(d)
        _factor(n // d)
    _factor(n)
    return factors

def generate_divisors(factors_dict):
    divisors = [1]
    for p, exp in factors_dict.items():
        temp = []
        p_pows = [p**e for e in range(exp + 1)]
        for d in divisors:
            for pow_p in p_pows:
                temp.append(d * pow_p)
        divisors = temp
    divisors = sorted(divisors)
    return divisors

def compute_fib_pair(n, mod):
    if n == 0:
        return (0, 1)
    x, y = 0, 1
    mask = 1 << (n.bit_length() - 1)
    while mask > 0:
        c = (x * (2 * y - x)) % mod
        d = (x * x + y * y) % mod
        if (n & mask) != 0:
            x, y = d, (c + d) % mod
        else:
            x, y = c, d
        mask >>= 1
    return (x, y)

def main():
    input = sys.stdin.read().split()
    ptr = 0
    N = int(input[ptr])
    ptr += 1
    lcm_factors = {}
    for _ in range(N):
        p = int(input[ptr])
        ptr += 1
        k = int(input[ptr])
        ptr += 1
        if p == 5:
            period_p = 20
            factors_pi_period = factor(period_p)
        else:
            rem = p % 5
            if rem in (1, 4):
                base = p - 1
            else:
                base = 2 * (p + 1)
            base_factors = factor(base)
            divisors = generate_divisors(base_factors)
            period_p = None
            for m in divisors:
                if m == 0:
                    continue
                a, b = compute_fib_pair(m, p)
                if a == 0 and b == 1:
                    period_p = m
                    break
            factors_pi_period = factor(period_p)
        period_pk_factors = factors_pi_period.copy()
        if p in period_pk_factors:
            period_pk_factors[p] += (k - 1)
        else:
            period_pk_factors[p] = (k - 1)
        for q, e in period_pk_factors.items():
            if q in lcm_factors:
                if e > lcm_factors[q]:
                    lcm_factors[q] = e
            else:
                lcm_factors[q] = e
    result = 1
    for q, e in lcm_factors.items():
        result = (result * pow(q, e, MOD)) % MOD
    print(result)

if __name__ == '__main__':
    main()
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