結果

問題 No.2013 Can we meet?
コンテスト
ユーザー Kiri8128
提出日時 2022-04-16 14:13:47
言語 PyPy3
(7.3.15)
結果
AC  
実行時間 1,480 ms / 2,500 ms
コード長 4,411 bytes
コンパイル時間 159 ms
コンパイル使用メモリ 82,456 KB
実行使用メモリ 183,372 KB
最終ジャッジ日時 2024-07-04 22:09:12
合計ジャッジ時間 20,341 ms
ジャッジサーバーID
（参考情報） 		judge4 / judge1
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 * 4
other AC * 35
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 # 

P = 998244353
p, g, ig = 998244353, 3, 332748118
W = [pow(g, (p - 1) >> i, p) for i in range(24)]
iW = [pow(ig, (p - 1) >> i, p) for i in range(24)]

def convolve(a, b):
    def fft(f):
        for l in range(k, 0, -1):
            d = 1 << l - 1
            U = [1]
            for i in range(d):
                U.append(U[-1] * W[l] % p)

            for i in range(1 << k - l):
                for j in range(d):
                    s = i * 2 * d + j
                    t = s + d
                    f[s], f[t] = (f[s] + f[t]) % p, U[j] * (f[s] - f[t]) % p

    def ifft(f):
        for l in range(1, k + 1):
            d = 1 << l - 1
            U = [1]
            for i in range(d):
                U.append(U[-1] * iW[l] % p)

            for i in range(1 << k - l):
                for j in range(d):
                    s = i * 2 * d + j
                    t = s + d
                    f[s], f[t] = (f[s] + f[t] * U[j]) % p, (f[s] - f[t] * U[j]) % p

    n0 = len(a) + len(b) - 1
    if len(a) < 80 or len(b) < 80:
        ret = [0] * n0
        if len(a) > len(b): a, b = b, a
        for i, aa in enumerate(a):
            for j, bb in enumerate(b):
                ret[i+j] = (ret[i+j] + aa * bb) % p
        return ret
    
    k = (n0).bit_length()
    n = 1 << k
    a = a + [0] * (n - len(a))
    b = b + [0] * (n - len(b))
    fft(a), fft(b)
    for i in range(n):
        a[i] = a[i] * b[i] % p
    ifft(a)
    invn = pow(n, p - 2, p)
    for i in range(n0):
        a[i] = a[i] * invn % p
    del a[n0:]
    return a

class SemiRelaxedMultiplication():
    # h = f * g
    # f: online
    # g: given
    def __init__(self, g):
        self.f = []
        self.g = g # コピーしていないので注意
        self.h = [0] * 8
        self.n = 0
    
    def calc(self, l, m):
        self.h += [0] * (l + 3 * m - 1 - len(self.h))
        co = convolve(self.f[l:l+m], self.g[m:2*m])
        for i, a in enumerate(co, l + m):
            self.h[i] = (self.h[i] + a) % p
        
    def append(self, a):
        # self.h += [0, 0]
        self.f.append(a)
        self.n += 1
        n = self.n
        self.h[n-1] = (self.h[n-1] + self.f[n-1] * self.g[0]) % P
        self.h[n] = (self.h[n] + self.f[n-1] * self.g[1]) % P
        s = n
        m = 2
        while n % m == 0:
            self.calc(s - m, m)
            m *= 2
        return self.h[n-1]

nn = 1001001

fa = [1] * (nn+1)
fainv = [1] * (nn+1)
for i in range(nn):
    fa[i+1] = fa[i] * (i+1) % P
fainv[-1] = pow(fa[-1], P-2, P)
for i in range(nn)[::-1]:
    fainv[i] = fainv[i+1] * (i+1) % P

C = lambda a, b: fa[a] * fainv[b] % P * fainv[a-b] % P if 0 <= b <= a else 0

def calc(n, x1, y1, x2, y2, a, b, L):
    x = abs(x1 - x2)
    y = abs(y1 - y2)
    if x + y > 2 * n:
        return 0
    if (x + y) % 2:
        return 0
    
    m = n - (x + y) // 2 + 1
    iv = pow(2 * (a + b), P - 2, P)
    alpha = a * iv % P
    beta = b * iv % P
    
    poa = [1]
    pob = [1]
    for i in range(n * 4 + 1):
        poa.append(poa[-1] * alpha % P)
    for i in range(n * 4 + 1):
        pob.append(pob[-1] * beta % P)
    
    assert (alpha + beta) * 2 % P == 1
    
    tmp1 = [fainv[x+k] * fainv[k] % P * poa[x+2*k] % P for k in range(m)]
    tmp2 = [fainv[y+l] * fainv[l] % P * pob[y+2*l] % P for l in range(m)]
    o = (x + y) // 2
    qq = ([0] * o + [fa[(o+i)*2] * a % P for i, a in enumerate(convolve(tmp1, tmp2))])[:n+1]
    tmp1 = [fainv[k] * fainv[k] % P * poa[2*k] % P for k in range(n + 1)]
    tmp2 = [fainv[l] * fainv[l] % P * pob[2*l] % P for l in range(n + 1)]
    ss = [fa[i*2] * a % P for i, a in enumerate(convolve(tmp1, tmp2))]
    ss1 = ss[1:2+n]
    srm = SemiRelaxedMultiplication(ss1)
    a = 0
    rr = [a]
    for b in ss1:
        a = (b - srm.append(a)) % P
        rr.append(a)
    
    qqrr = convolve(qq, rr)
    pp = [(a - b) % P for a, b in zip(qq, qqrr)]
    
    ans = 0
    for i in range(n):
        ans = (ans + pp[i+1] * L[i]) % P
    
    return ans


N = int(input())
x1, y1, x2, y2 = map(int, input().split())
a, b = map(int, input().split())

A = [int(a) for a in input().split()]
print(calc(N, x1, y1, x2, y2, a, b, A))

# Check
assert 1 <= N <= 10 ** 5
assert 0 <= x1 <= 10 ** 9
assert 0 <= y1 <= 10 ** 9
assert 0 <= x2 <= 10 ** 9
assert 0 <= y2 <= 10 ** 9
assert (x1, y1) != (x2, y2)
assert 1 <= a <= 10 ** 6
assert 1 <= b <= 10 ** 6
for aa in A:
    assert 1 <= aa <= 10 ** 9
0