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 17:23:36
言語 PyPy3
(7.3.15)
結果
RE  
実行時間 -
コード長 4,028 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 207 ms
コンパイル使用メモリ 82,640 KB
実行使用メモリ 70,292 KB
最終ジャッジ日時 2025-03-31 17:23:57
合計ジャッジ時間 2,717 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 #
raw source code 

import sys
import math
import random
from functools import reduce

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, 3, 5, 7, 11]:
        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 sorted(factors)

def generate_divisors(factors):
    from collections import defaultdict
    factor_counts = defaultdict(int)
    for p in factors:
        factor_counts[p] += 1
    divisors = [1]
    for p in factor_counts:
        exponents = [p**e for e in range(factor_counts[p] + 1)]
        new_divisors = []
        for d in divisors:
            for exp in exponents:
                new_divisors.append(d * exp)
        divisors = new_divisors
    divisors = sorted(divisors)
    return divisors

def multiply(a, b, mod):
    return [
        [(a[0][0]*b[0][0] + a[0][1]*b[1][0]) % mod,
         (a[0][0]*b[0][1] + a[0][1]*b[1][1]) % mod],
        [(a[1][0]*b[0][0] + a[1][1]*b[1][0]) % mod,
         (a[1][0]*b[0][1] + a[1][1]*b[1][1]) % mod]
    ]

def matrix_pow(mat, power, mod):
    result = [[1, 0], [0, 1]]
    while power > 0:
        if power % 2 == 1:
            result = multiply(result, mat, mod)
        mat = multiply(mat, mat, mod)
        power //= 2
    return result

def compute_fibs(d, mod):
    if d == 0:
        return (0, 1)
    if mod == 1:
        return (0, 0)
    result = [[1, 0], [0, 1]]
    mat = [[1, 1], [1, 0]]
    power = d
    while power > 0:
        if power % 2 == 1:
            result = multiply(result, mat, mod)
        mat = multiply(mat, mat, mod)
        power //= 2
    Fd_plus_1 = result[0][0]
    Fd = result[0][1]
    return (Fd % mod, Fd_plus_1 % mod)

def main():
    input = sys.stdin.read().split()
    ptr = 0
    n = int(input[ptr])
    ptr +=1
    primes = []
    for _ in range(n):
        p = int(input[ptr])
        k = int(input[ptr+1])
        ptr +=2
        primes.append( (p, k) )
    periods = []
    for p, k in primes:
        if p == 2:
            per = 3 * (2 ** (k-1))
            periods.append(per)
            continue
        if p == 5:
            per = 4 * (5 ** k)
            periods.append(per)
            continue
        legendre = pow(5, (p-1)//2, p)
        m = 0
        if legendre == 1 or legendre == 0:
            m = p -1
        else:
            m = 2 * (p +1)
        factors = factor(m)
        divisors = generate_divisors(factors)
        correct_d = None
        for d in divisors:
            if d ==0:
                Fd = 0
                Fd_next = 1 % p
            else:
                Fd, Fd_next = compute_fibs(d, p)
            if Fd % p ==0 and Fd_next % p ==1:
                correct_d = d
                break
        if correct_d is None:
            correct_d =0
        per_p = correct_d
        per_i = per_p * (p ** (k-1))
        periods.append(per_i)
    def lcm(a, b):
        return a * b // math.gcd(a, b)
    total = reduce(lcm, periods, 1)
    print(total % MOD)

if __name__ == "__main__":
    main()
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