結果

問題 No.2120 場合の数の下８桁
ユーザー 👑 rin204rin204
提出日時 2022-11-04 21:34:43
言語 PyPy3
(7.3.15)
結果
AC  
実行時間 191 ms / 2,000 ms
コード長 4,015 bytes
コンパイル時間 121 ms
コンパイル使用メモリ 82,260 KB
実行使用メモリ 82,304 KB
最終ジャッジ日時 2024-07-18 19:17:36
合計ジャッジ時間 4,651 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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テストケース

テストケース表示
入力 結果 実行時間
実行使用メモリ
testcase_00 AC 190 ms
82,048 KB
testcase_01 AC 181 ms
82,048 KB
testcase_02 AC 187 ms
82,176 KB
testcase_03 AC 186 ms
81,920 KB
testcase_04 AC 180 ms
81,920 KB
testcase_05 AC 180 ms
82,048 KB
testcase_06 AC 182 ms
82,176 KB
testcase_07 AC 184 ms
81,920 KB
testcase_08 AC 183 ms
81,920 KB
testcase_09 AC 185 ms
82,048 KB
testcase_10 AC 187 ms
81,792 KB
testcase_11 AC 183 ms
81,920 KB
testcase_12 AC 184 ms
81,664 KB
testcase_13 AC 185 ms
82,304 KB
testcase_14 AC 182 ms
81,664 KB
testcase_15 AC 183 ms
82,048 KB
testcase_16 AC 189 ms
82,176 KB
testcase_17 AC 184 ms
82,048 KB
testcase_18 AC 191 ms
82,176 KB
testcase_19 AC 191 ms
81,792 KB
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 # 

from math import gcd

def isprime(n):
    if n <= 1:
        return False
    elif n == 2:
        return True
    elif n % 2 == 0:
        return False
    
    A = [2, 325, 9375, 28178, 450775, 9780504, 1795265022]
    s = 0
    d = n - 1
    while d % 2 == 0:
        s += 1
        d >>= 1
    
    for a in A:
        if a % n == 0:
            return True
        x = pow(a, d, n)
        if x != 1:
            for t in range(s):
                if x == n - 1:
                    break
                x = x * x % n
            else:
                return False
    return True
        
def pollard(n):
    if n % 2 == 0:
        return 2
    if isprime(n):
        return n
    
    f = lambda x:(x * x + 1) % n
    
    step = 0
    while 1:
        step += 1
        x = step
        y = f(x)
        while 1:
            p = gcd(y - x + n, n)
            if p == 0 or p == n:
                break
            if p != 1:
                return p
            x = f(x)
            y = f(f(y))

def primefact(n):
    if n == 1:
        return []
    p = pollard(n)
    if p == n:
        return [p]
    left = primefact(p)
    right = primefact(n // p)
    left += right
    return sorted(left)

def modinv(a, MOD):
    b = MOD
    u = 1
    v = 0
    while b:
        t = a // b
        a -= t * b
        u -= t * v
        a, b = b, a
        u, v = v, u
    u %= MOD
    return u

def Garner(M, R):
    if not M:
        return 0
    m_prod = M[0]
    C = R[0]
    for m, r in zip(M[1:], R[1:]):
        t = (r - C) * modinv(m_prod, m) % m
        C += t * m_prod
        m_prod *= m
    return C

class Combination_Arbitary_sub:
    def __init__(self, p, pq):
        self.fact = [0] * (pq + 1)
        self.invfact = [0] * (pq + 1)
        self.fact[0] = 1
        self.invfact[0] = 1
        for i in range(1, pq + 1):
            if i % p == 0:
                self.fact[i] = self.fact[i - 1]
            else:
                self.fact[i] = self.fact[i - 1] * i % pq
            self.invfact[i] = modinv(self.fact[i], pq)

class Combination_Arbitary:
    def __init__(self, MOD):
        self.MOD = MOD
        primes = primefact(MOD)
        self.le = len(set(primes))
        self.p = sorted(set(primes))
        self.q = [0] * self.le
        self.pq = [1] * self.le
        ind = -1
        bef = -1
        for p in primes:
            if p != bef:
                bef = p
                ind += 1
            self.q[ind] += 1
            self.pq[ind] *= p
        self.fac = [None] * self.le
        for i, (p_, pq_) in enumerate(zip(self.p, self.pq)):
            self.fac[i] = Combination_Arbitary_sub(p_, pq_)
    
    def C(self, n, k, p, q, pq, fac):
        z = n - k
        
        e0 = 0
        u = n // p
        while u > 0:
            e0 += u
            u //= p
        u = k // p
        while u > 0:
            e0 -= u
            u //= p
        u = z // p
        while u > 0:
            e0 -= u
            u //= p

        em = 0
        u = n // pq
        while u > 0:
            em += u
            u //= p
        u = k // pq
        while u > 0:
            em -= u
            u //= p
        u = z // pq
        while u > 0:
            em -= u
            u //= p

        ret = 1
        while n > 0:
            ret *= fac.fact[n % pq]
            ret %= pq
            ret *= fac.invfact[k % pq]
            ret %= pq
            ret *= fac.invfact[z % pq]
            ret %= pq
            n //= p
            k //= p
            z //= p
        ret *= pow(p, e0, pq)
        ret %= pq
        if(not(p == 2 and q >= 3) and em & 1):
            ret = -ret % pq
        return ret

    def nCk(self, n, k):
        if n < k or k < 0:
            return 0
        
        R = [0] * self.le
        for i in range(self.le):
            R[i] = self.C(n, k, self.p[i], self.q[i], self.pq[i], self.fac[i])
        return Garner(self.pq, R)

m = int(input())
n = int(input())
Comb = Combination_Arbitary(10 ** 8)
ans = str(Comb.nCk(m, n)).zfill(8)
print(ans)
0