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 15:33:38
言語 PyPy3
(7.3.15)
結果
RE  
実行時間 -
コード長 4,022 bytes
コンパイル時間 275 ms
コンパイル使用メモリ 82,316 KB
実行使用メモリ 70,996 KB
最終ジャッジ日時 2025-06-12 15:34:57
合計ジャッジ時間 2,348 ms
ジャッジサーバーID
（参考情報） 		judge4 / judge3
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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
import math

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)
    factors.sort()
    return factors

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

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

def matrix_mult(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 = matrix_mult(result, mat, mod)
        mat = matrix_mult(mat, mat, mod)
        power = power // 2
    return result

def compute_fib_d(d, p):
    if d == 0:
        return (0, 1)
    mat = [[1, 1], [1, 0]]
    mat_d = matrix_pow(mat, d, p)
    fib_d = mat_d[1][0]
    fib_d_plus1 = mat_d[0][0]
    return (fib_d % p, fib_d_plus1 % p)

def compute_pisano(p):
    if p == 2:
        return 3
    if p == 5:
        return 20
    mod = p % 5
    if mod == 1 or mod == 4:
        n = p - 1
    else:
        n = 2 * (p + 1)
    if n == 0:
        return 1
    factors = factorize(n)
    divisors = generate_divisors(factors)
    for d in divisors:
        if d == 0:
            continue
        fib_d, fib_d_plus1 = compute_fib_d(d, p)
        if fib_d == 0 and fib_d_plus1 == 1:
            return d
    return n

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:
            period = 3 * (2 ** (k -1))
        elif p ==5:
            period = 20 * (5 ** (k-1))
        else:
            if not is_prime(p):
                raise ValueError("p must be prime.")
            base = compute_pisano(p)
            period = base * (p ** (k-1))
        pisano_periods.append( period )
    def gcd(a, b):
        while b:
            a, b = b, a % b
        return a
    def lcm(a, b):
        return a * b // gcd(a, b)
    result = 1
    for period in pisano_periods:
        result = lcm(result, period)
    result %= MOD
    print(result)

if __name__ == '__main__':
    main()
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