結果

問題 No.890 移調の限られた旋法
ユーザー lam6er
提出日時 2025-03-26 15:48:52
言語 PyPy3
(7.3.15)
結果
AC  
実行時間 65 ms / 2,000 ms
コード長 2,409 bytes
コンパイル時間 161 ms
コンパイル使用メモリ 82,376 KB
実行使用メモリ 76,400 KB
最終ジャッジ日時 2025-03-26 15:49:55
合計ジャッジ時間 3,183 ms
ジャッジサーバーID
（参考情報） 		judge1 / 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 AC * 3
other AC * 32
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 # 

MOD = 10**9 + 7

def main():
    import sys
    N, K = map(int, sys.stdin.readline().split())
    
    # Precompute factorial and inverse factorial modulo MOD
    max_n = N
    fact = [1] * (max_n + 1)
    for i in range(1, max_n + 1):
        fact[i] = fact[i-1] * i % MOD
    inv_fact = [1] * (max_n + 1)
    inv_fact[max_n] = pow(fact[max_n], MOD-2, MOD)
    for i in range(max_n-1, -1, -1):
        inv_fact[i] = inv_fact[i+1] * (i+1) % MOD
    
    def comb(n, k):
        if n < 0 or k < 0 or k > n:
            return 0
        return fact[n] * inv_fact[k] % MOD * inv_fact[n - k] % MOD
    
    # Find all divisors d > 1 of N
    divisors = []
    n = N
    i = 2
    while i * i <= n:
        if n % i == 0:
            divisors.append(i)
            while n % i == 0:
                n //= i
        i += 1
    if n > 1:
        divisors.append(n)
    # Function to generate all divisors >1 using the prime factors
    from itertools import product
    primes = {}
    n = N
    for p in divisors:
        cnt = 0
        while n % p == 0:
            cnt += 1
            n //= p
        primes[p] = cnt
    # Regenerate the list of unique prime factors
    unique_primes = list(primes.keys())
    # Generate all divisors >1
    all_d = [1]
    for p in unique_primes:
        exponents = [p**e for e in range(1, primes[p]+1)]
        new_divs = []
        for d in all_d:
            for exp in exponents:
                new_divs.append(d * exp)
        all_d += new_divs
    all_d = list(set(all_d))
    all_d = [d for d in all_d if d > 1]
    
    total = 0
    for d in all_d:
        if K % d != 0:
            continue
        # Compute mu(d)
        mu = 1
        temp = d
        for p in unique_primes:
            if temp % p == 0:
                cnt = 0
                while temp % p == 0:
                    cnt += 1
                    temp //= p
                if cnt >= 2:
                    mu = 0
                    break
                mu *= -1
        if temp != 1:
            # d has a prime factor not in primes, which is impossible
            pass
        if mu == 0:
            continue
        # Compute combination
        n_div = N // d
        k_div = K // d
        c = comb(n_div, k_div)
        total += mu * c
        total %= MOD
    
    # The answer is (-total) mod MOD
    ans = (-total) % MOD
    print(ans)
    
if __name__ == '__main__':
    main()
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