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 14:28:23
言語 PyPy3
(7.3.15)
結果
RE  
実行時間 -
コード長 3,899 bytes
コンパイル時間 276 ms
コンパイル使用メモリ 82,360 KB
実行使用メモリ 70,496 KB
最終ジャッジ日時 2025-06-12 14:28:34
合計ジャッジ時間 2,531 ms
ジャッジサーバーID
（参考情報） 		judge3 / judge4
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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 math
import random
from heapq import heappush, heappop

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, 13, 17, 19, 23, 29, 31]:
        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[n] = factors.get(n, 0) + 1
            return
        d = pollards_rho(n)
        _factor(d)
        _factor(n // d)
    _factor(n)
    return factors

def generate_divisors_sorted(factors_dict):
    primes = sorted(factors_dict.keys())
    divisors = [1]
    for p in primes:
        exp = factors_dict[p]
        temp = []
        for d in divisors:
            current = 1
            for _ in range(exp + 1):
                temp.append(d * current)
                current *= p
        divisors = sorted(temp)
    return divisors

def matrix_mult(a, b, mod):
    return [
        (a[0]*b[0] + a[1]*b[2]) % mod,
        (a[0]*b[1] + a[1]*b[3]) % mod,
        (a[2]*b[0] + a[3]*b[2]) % mod,
        (a[2]*b[1] + a[3]*b[3]) % mod,
    ]

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

def fib_mod(n, mod_value):
    if n == 0:
        return (0, 1)
    matrix = [1, 1, 1, 0]
    powered = matrix_pow(matrix, n, mod_value)
    return (powered[1], powered[0])

def get_pisano_period(p):
    if p == 2:
        return 3
    if p == 5:
        return 20
    if p % 5 in (1, 4):
        m = p - 1
    else:
        m = 2 * (p + 1)
    m_factors = factor(m)
    divisors = generate_divisors_sorted(m_factors)
    for d in divisors:
        if d == 0:
            continue
        fn, fn1 = fib_mod(d, p)
        if fn == 0 and fn1 % p == 1:
            return d
    return m

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))
    
    global_factors = {}
    for p, k in primes:
        if p == 2:
            if k == 1:
                factors = {3: 1}
            else:
                factors = {2: k-1, 3: 1}
        elif p == 5:
            factors = {2: 2, 5: k}
        else:
            d = get_pisano_period(p)
            d_factors = factor(d)
            if p in d_factors:
                d_factors[p] += k - 1
            else:
                d_factors[p] = k - 1
            factors = d_factors
        
        for q, exp in factors.items():
            if q in global_factors:
                if exp > global_factors[q]:
                    global_factors[q] = exp
            else:
                global_factors[q] = exp
    
    result = 1
    for q, exp in global_factors.items():
        result = (result * pow(q, exp, MOD)) % MOD
    print(result)

if __name__ == "__main__":
    main()
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