結果

問題 No.3038 シャッフルの再現
コンテスト
ユーザー lam6er
提出日時 2025-03-31 17:39:58
言語 PyPy3
(7.3.15)
結果
RE  
実行時間 -
コード長 3,836 bytes
記録
記録タグの例:
初AC ショートコード 純ショートコード 純主流ショートコード 最速実行時間
コンパイル時間 151 ms
コンパイル使用メモリ 82,776 KB
実行使用メモリ 70,692 KB
最終ジャッジ日時 2025-03-31 17:40:45
合計ジャッジ時間 2,326 ms
ジャッジサーバーID
（参考情報） 		judge4 / judge5
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 #
raw source code 

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]:
        if n % p == 0:
            return n == p
    d = n - 1
    s = 0
    while d % 2 == 0:
        d //= 2
        s += 1
    for a in [2,325,9375,28178,450775,9780504,1795265022]:
        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 trial_division(n):
    factors = {}
    while n % 2 == 0:
        factors[2] = factors.get(2, 0) + 1
        n = n // 2
    i = 3
    while i*i <= n and n > 1:
        while n % i == 0:
            factors[i] = factors.get(i, 0) + 1
            n = n // i
        i += 2
    if n > 1:
        factors[n] = 1
    return factors

def factorize(n):
    if n == 0:
        return {}
    factors = trial_division(n)
    remaining = 1
    for p in list(factors.keys()):
        remaining *= p ** factors[p]
    if remaining != 1 and n != remaining:
        remaining = n // remaining
        if remaining != 1:
            big_factors = factor(remaining)
            for p in big_factors:
                factors[p] = factors.get(p, 0) + big_factors[p]
    return factors

def generate_divisors(factors):
    primes = sorted(factors.keys())
    divisors = [1]
    for p in primes:
        exp = factors[p]
        current_p_pows = [p**e for e in range(1, exp+1)]
        temp = []
        for d in divisors:
            for pow_val in current_p_pows:
                temp.append(d * pow_val)
        divisors += temp
    divisors = sorted(divisors)
    return divisors

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

def compute_pi(p):
    if p == 5:
        return 20
    rem = p % 5
    if rem in [1, 4]:
        s = p - 1
    else:
        s = 2 * (p + 1)
    factors = factorize(s)
    divisors = generate_divisors(factors)
    for d in divisors:
        if d == 0:
            continue
        fn, fn_plus_1 = fast_doubling(d, p)
        if fn % p == 0 and fn_plus_1 % p == 1:
            return d
    return s

def main():
    input = sys.stdin.read().split()
    idx = 0
    n_case = int(input[idx])
    idx += 1
    factors_M = []
    for _ in range(n_case):
        p = int(input[idx])
        k = int(input[idx+1])
        factors_M.append((p, k))
        idx +=2

    periods = []
    for (p, k) in factors_M:
        if p == 5:
            pi_p = 20
        else:
            pi_p = compute_pi(p)
        current_period = pi_p * pow(p, k-1)
        periods.append(current_period)
    
    def lcm(a, b):
        return a * b // gcd(a, b)
    
    result = 1
    for period in periods:
        result = lcm(result, period) % MOD
    print(result % MOD)

if __name__ == "__main__":
    main()
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