結果

問題 No.2013 Can we meet?
ユーザー chineristACchineristAC
提出日時 2022-07-15 23:24:52
言語 PyPy3
(7.3.13)
結果
AC  
実行時間 1,672 ms / 2,500 ms
コード長 10,727 bytes
コンパイル時間 284 ms
コンパイル使用メモリ 87,068 KB
実行使用メモリ 285,488 KB
最終ジャッジ日時 2023-09-10 05:18:20
合計ジャッジ時間 32,217 ms
ジャッジサーバーID
(参考情報)
judge14 / judge12
このコードへのチャレンジ(β)

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 146 ms
88,460 KB
testcase_01 AC 149 ms
88,432 KB
testcase_02 AC 148 ms
88,652 KB
testcase_03 AC 150 ms
88,364 KB
testcase_04 AC 147 ms
88,616 KB
testcase_05 AC 148 ms
88,368 KB
testcase_06 AC 148 ms
88,352 KB
testcase_07 AC 149 ms
88,616 KB
testcase_08 AC 149 ms
88,328 KB
testcase_09 AC 151 ms
88,384 KB
testcase_10 AC 151 ms
88,376 KB
testcase_11 AC 155 ms
88,616 KB
testcase_12 AC 154 ms
89,024 KB
testcase_13 AC 154 ms
88,892 KB
testcase_14 AC 233 ms
93,008 KB
testcase_15 AC 231 ms
92,960 KB
testcase_16 AC 236 ms
93,064 KB
testcase_17 AC 235 ms
92,732 KB
testcase_18 AC 237 ms
93,048 KB
testcase_19 AC 233 ms
93,060 KB
testcase_20 AC 234 ms
93,148 KB
testcase_21 AC 235 ms
93,160 KB
testcase_22 AC 236 ms
93,312 KB
testcase_23 AC 237 ms
92,764 KB
testcase_24 AC 1,672 ms
279,408 KB
testcase_25 AC 1,567 ms
282,268 KB
testcase_26 AC 1,576 ms
282,280 KB
testcase_27 AC 1,574 ms
282,196 KB
testcase_28 AC 1,557 ms
282,396 KB
testcase_29 AC 1,581 ms
282,096 KB
testcase_30 AC 1,564 ms
282,140 KB
testcase_31 AC 1,575 ms
282,420 KB
testcase_32 AC 1,576 ms
282,280 KB
testcase_33 AC 1,609 ms
285,488 KB
testcase_34 AC 1,655 ms
283,700 KB
testcase_35 AC 1,639 ms
281,436 KB
testcase_36 AC 1,569 ms
283,720 KB
testcase_37 AC 1,581 ms
280,796 KB
testcase_38 AC 1,618 ms
280,620 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 #

mod = 998244353
omega = pow(3,119,mod)
rev_omega = pow(omega,mod-2,mod)

N = 2*10**5
g1 = [1]*(N+1) # 元テーブル
g2 = [1]*(N+1) #逆元テーブル
inv = [1]*(N+1) #逆元テーブル計算用テーブル

for i in range( 2, N + 1 ):
    g1[i]=( ( g1[i-1] * i ) % mod )
    inv[i]=( ( -inv[mod % i] * (mod//i) ) % mod )
    g2[i]=( (g2[i-1] * inv[i]) % mod )
inv[0]=0

def _ntt(f,L,reverse=False):
    F=[f[i] for i in range(L)]
    n = L.bit_length() - 1
    base = omega
    if reverse:
        base = rev_omega

    if not n:
        return F

    size = 2**n
    wj = pow(base,2**22,mod)
    res = [0]*2**n

    for i in range(n,0,-1):
        use_omega = pow(base,2**(22+i-n),mod)
        res = [0]*2**n
        size //= 2
        w = 1
        for j in range(0,L//2,size):
            for a in range(size):
                res[a+j] = (F[a+2*j] + w * F[a+size+2*j]) % mod
                t = (w * wj) % mod
                res[L//2+a+j] = (F[a+2*j] + t * F[a+size+2*j]) % mod
            w = (w * use_omega) % mod
        F = res

    return res

def ntt(f,L=0):
    l = len(f)
    if not L:
        L = 1<<((l-1).bit_length())
    while len(f)<L:
        f.append(0)
    f=f[:L]
    F = _ntt(f,L)
    return F

def intt(f,L=0):
    l = len(f)
    if not L:
        L = 1<<((l-1).bit_length())
    while len(f)<L:
        f.append(0)
    f=f[:L]
    F = _ntt(f,L,reverse=True)
    inv = pow(L,mod-2,mod)
    for i in range(L):
        F[i] *= inv
        F[i] %= mod
    return F

def convolve(_f,_g,limit):
    f = [v for v in _f]
    g = [v for v in _g]
    l = len(f)+len(g)-1
    L = 1<<((l-1).bit_length())

    F = ntt(f,L)
    G = ntt(g,L)

    H = [(F[i] * G[i]) % mod for i in range(L)]

    h = intt(H,L)

    return h[:limit]

mod = 998244353
omega = pow(3,119,mod)
rev_omega = pow(omega,mod-2,mod)

N = 2*10**5
g1 = [1]*(N+1) # 元テーブル
g2 = [1]*(N+1) #逆元テーブル
inv = [1]*(N+1) #逆元テーブル計算用テーブル

for i in range( 2, N + 1 ):
    g1[i]=( ( g1[i-1] * i ) % mod )
    inv[i]=( ( -inv[mod % i] * (mod//i) ) % mod )
    g2[i]=( (g2[i-1] * inv[i]) % mod )
inv[0]=0

_fft_mod = 998244353
_fft_imag = 911660635
_fft_iimag = 86583718
_fft_rate2 = (911660635, 509520358, 369330050, 332049552, 983190778, 123842337, 238493703, 975955924, 603855026, 856644456, 131300601,
              842657263, 730768835, 942482514, 806263778, 151565301, 510815449, 503497456, 743006876, 741047443, 56250497, 867605899)
_fft_irate2 = (86583718, 372528824, 373294451, 645684063, 112220581, 692852209, 155456985, 797128860, 90816748, 860285882, 927414960,
               354738543, 109331171, 293255632, 535113200, 308540755, 121186627, 608385704, 438932459, 359477183, 824071951, 103369235)
_fft_rate3 = (372528824, 337190230, 454590761, 816400692, 578227951, 180142363, 83780245, 6597683, 70046822, 623238099,
              183021267, 402682409, 631680428, 344509872, 689220186, 365017329, 774342554, 729444058, 102986190, 128751033, 395565204)
_fft_irate3 = (509520358, 929031873, 170256584, 839780419, 282974284, 395914482, 444904435, 72135471, 638914820, 66769500,
               771127074, 985925487, 262319669, 262341272, 625870173, 768022760, 859816005, 914661783, 430819711, 272774365, 530924681)
 
 
def _butterfly(a):
    n = len(a)
    h = (n - 1).bit_length()
    len_ = 0
    while len_ < h:
        if h - len_ == 1:
            p = 1 << (h - len_ - 1)
            rot = 1
            for s in range(1 << len_):
                offset = s << (h - len_)
                for i in range(p):
                    l = a[i + offset]
                    r = a[i + offset + p] * rot % _fft_mod
                    a[i + offset] = (l + r) % _fft_mod
                    a[i + offset + p] = (l - r) % _fft_mod
                if s + 1 != (1 << len_):
                    rot *= _fft_rate2[(~s & -~s).bit_length() - 1]
                    rot %= _fft_mod
            len_ += 1
        else:
            p = 1 << (h - len_ - 2)
            rot = 1
            for s in range(1 << len_):
                rot2 = rot * rot % _fft_mod
                rot3 = rot2 * rot % _fft_mod
                offset = s << (h - len_)
                for i in range(p):
                    a0 = a[i + offset]
                    a1 = a[i + offset + p] * rot
                    a2 = a[i + offset + p * 2] * rot2
                    a3 = a[i + offset + p * 3] * rot3
                    a1na3imag = (a1 - a3) % _fft_mod * _fft_imag
                    a[i + offset] = (a0 + a2 + a1 + a3) % _fft_mod
                    a[i + offset + p] = (a0 + a2 - a1 - a3) % _fft_mod
                    a[i + offset + p * 2] = (a0 - a2 + a1na3imag) % _fft_mod
                    a[i + offset + p * 3] = (a0 - a2 - a1na3imag) % _fft_mod
                if s + 1 != (1 << len_):
                    rot *= _fft_rate3[(~s & -~s).bit_length() - 1]
                    rot %= _fft_mod
            len_ += 2
 
 
def _butterfly_inv(a):
    n = len(a)
    h = (n - 1).bit_length()
    len_ = h
    while len_:
        if len_ == 1:
            p = 1 << (h - len_)
            irot = 1
            for s in range(1 << (len_ - 1)):
                offset = s << (h - len_ + 1)
                for i in range(p):
                    l = a[i + offset]
                    r = a[i + offset + p]
                    a[i + offset] = (l + r) % _fft_mod
                    a[i + offset + p] = (l - r) * irot % _fft_mod
                if s + 1 != (1 << (len_ - 1)):
                    irot *= _fft_irate2[(~s & -~s).bit_length() - 1]
                    irot %= _fft_mod
            len_ -= 1
        else:
            p = 1 << (h - len_)
            irot = 1
            for s in range(1 << (len_ - 2)):
                irot2 = irot * irot % _fft_mod
                irot3 = irot2 * irot % _fft_mod
                offset = s << (h - len_ + 2)
                for i in range(p):
                    a0 = a[i + offset]
                    a1 = a[i + offset + p]
                    a2 = a[i + offset + p * 2]
                    a3 = a[i + offset + p * 3]
                    a2na3iimag = (a2 - a3) * _fft_iimag % _fft_mod
                    a[i + offset] = (a0 + a1 + a2 + a3) % _fft_mod
                    a[i + offset + p] = (a0 - a1 +
                                         a2na3iimag) * irot % _fft_mod
                    a[i + offset + p * 2] = (a0 + a1 -
                                             a2 - a3) * irot2 % _fft_mod
                    a[i + offset + p * 3] = (a0 - a1 -
                                             a2na3iimag) * irot3 % _fft_mod
                if s + 1 != (1 << (len_ - 1)):
                    irot *= _fft_irate3[(~s & -~s).bit_length() - 1]
                    irot %= _fft_mod
            len_ -= 2
 
 
def _convolution_naive(a, b):
    n = len(a)
    m = len(b)
    ans = [0] * (n + m - 1)
    if n < m:
        for j in range(m):
            for i in range(n):
                ans[i + j] = (ans[i + j] + a[i] * b[j]) % _fft_mod
    else:
        for i in range(n):
            for j in range(m):
                ans[i + j] = (ans[i + j] + a[i] * b[j]) % _fft_mod
    return ans
 
 
def _convolution_fft(a, b):
    a = a.copy()
    b = b.copy()
    n = len(a)
    m = len(b)
    z = 1 << (n + m - 2).bit_length()
    a += [0] * (z - n)
    _butterfly(a)
    b += [0] * (z - m)
    _butterfly(b)
    for i in range(z):
        a[i] = a[i] * b[i] % _fft_mod
    _butterfly_inv(a)
    a = a[:n + m - 1]
    iz = pow(z, _fft_mod - 2, _fft_mod)
    for i in range(n + m - 1):
        a[i] = a[i] * iz % _fft_mod
    return a
 
 
def _convolution_square(a):
    a = a.copy()
    n = len(a)
    z = 1 << (2 * n - 2).bit_length()
    a += [0] * (z - n)
    _butterfly(a)
    for i in range(z):
        a[i] = a[i] * a[i] % _fft_mod
    _butterfly_inv(a)
    a = a[:2 * n - 1]
    iz = pow(z, _fft_mod - 2, _fft_mod)
    for i in range(2 * n - 1):
        a[i] = a[i] * iz % _fft_mod
    return a
 
 
def convolution(a, b):
    """It calculates (+, x) convolution in mod 998244353. 
    Given two arrays a[0], a[1], ..., a[n - 1] and b[0], b[1], ..., b[m - 1], 
    it calculates the array c of length n + m - 1, defined by
 
    >   c[i] = sum(a[j] * b[i - j] for j in range(i + 1)) % 998244353.
 
    It returns an empty list if at least one of a and b are empty.
 
    Constraints
    -----------
 
    >   len(a) + len(b) <= 8388609
 
    Complexity
    ----------
 
    >   O(n log n), where n = len(a) + len(b).
    """
    n = len(a)
    m = len(b)
    if n == 0 or m == 0:
        return []
    if min(n, m) <= 0:
        return _convolution_naive(a, b)
    if a is b:
        return _convolution_square(a)
    return _convolution_fft(a, b)


def taylor_shift(f,a):
    g = [f[i]*g1[i]%mod for i in range(len(f))][::-1]
    e = [g2[i] for i in range(len(f))]
    t = 1
    for i in range(1,len(f)):
        t = t * a % mod
        e[i] = e[i] * t % mod
    
    res = convolution(g,e)[:len(f)]
    return [res[len(f)-1-i]*g2[i]%mod for i in range(len(f))]

def inverse(f,limit):
    assert(f[0]!=0)
    l = len(f)
    L = 1<<((l-1).bit_length())
    n = L.bit_length()-1
    f = f[:L]
    f+=[0]*(L-len(f))

    res = [pow(f[0],mod-2,mod)]
    for i in range(1,n+1):
        h = convolve(res,f[:2**i],2**i)
        h = [(-h[i]) % mod for i in range(2**i)]
        h[0] = (h[0]+2) % mod
        res = convolve(res,h,2**i)
    return res[:limit]


import sys,random,bisect
from collections import deque,defaultdict
from heapq import heapify,heappop,heappush
from itertools import permutations
from math import log,gcd

input = lambda :sys.stdin.readline().rstrip()
mi = lambda :map(int,input().split())
li = lambda :list(mi())

def cmb(n,r):
    if r < 0 or n < r:
        return 0
    return g1[n] * (g2[n-r] * g2[r] % mod) % mod

N = int(input())
a,b,c,d = mi()
A,B = mi()

P = li()

p,q = abs(c-a),abs(d-b)

x,y = A*pow(2*A+2*B,mod-2,mod) % mod,B*pow(2*A+2*B,mod-2,mod) % mod

X = [0] * (2*N+1)
Y = [0] * (2*N+1)

for i in range(2*N+1):
    if 2*i+p <= 2*N:
        X[2*i+p] = (g2[i] * g2[i+p] % mod) * pow(x,2*i+p,mod) % mod
    if 2*i+q <= 2*N:
        Y[2*i+q] = (g2[i] * g2[i+q] % mod) * pow(y,2*i+q,mod) % mod

XY = convolve(X,Y,2*N+1)

f = [0] * (N+1)
for i in range(N+1):
    f[i] = XY[2*i] * g1[2*i] % mod

p,q = 0,0

X = [0] * (2*N+1)
Y = [0] * (2*N+1)

for i in range(2*N+1):
    if 2*i+p <= 2*N:
        X[2*i+p] = (g2[i] * g2[i+p] % mod) * pow(x,2*i+p,mod) % mod
    if 2*i+q <= 2*N:
        Y[2*i+q] = (g2[i] * g2[i+q] % mod) * pow(y,2*i+q,mod) % mod

XY = convolve(X,Y,2*N+1)
g = [0] * (N+1)
for i in range(N+1):
    g[i] = XY[2*i] * g1[2*i] % mod



ig = inverse(g,N+1)
h = convolve(f,ig,N+1)

res = 0
for i in range(N):
    res += h[i+1] * P[i]
    res %= mod

print(res)

0