結果
問題 | No.2013 Can we meet? |
ユーザー |
|
提出日時 | 2022-07-15 23:24:52 |
言語 | PyPy3 (7.3.15) |
結果 |
AC
|
実行時間 | 1,704 ms / 2,500 ms |
コード長 | 10,727 bytes |
コンパイル時間 | 234 ms |
コンパイル使用メモリ | 82,432 KB |
実行使用メモリ | 281,744 KB |
最終ジャッジ日時 | 2024-06-27 20:54:37 |
合計ジャッジ時間 | 28,889 ms |
ジャッジサーバーID (参考情報) |
judge2 / judge1 |
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ファイルパターン | 結果 |
---|---|
sample | AC * 4 |
other | AC * 35 |
ソースコード
mod = 998244353omega = pow(3,119,mod)rev_omega = pow(omega,mod-2,mod)N = 2*10**5g1 = [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]=0def _ntt(f,L,reverse=False):F=[f[i] for i in range(L)]n = L.bit_length() - 1base = omegaif reverse:base = rev_omegaif not n:return Fsize = 2**nwj = pow(base,2**22,mod)res = [0]*2**nfor i in range(n,0,-1):use_omega = pow(base,2**(22+i-n),mod)res = [0]*2**nsize //= 2w = 1for 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]) % modt = (w * wj) % modres[L//2+a+j] = (F[a+2*j] + t * F[a+size+2*j]) % modw = (w * use_omega) % modF = resreturn resdef 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 Fdef 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] *= invF[i] %= modreturn Fdef convolve(_f,_g,limit):f = [v for v in _f]g = [v for v in _g]l = len(f)+len(g)-1L = 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 = 998244353omega = pow(3,119,mod)rev_omega = pow(omega,mod-2,mod)N = 2*10**5g1 = [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_ = 0while len_ < h:if h - len_ == 1:p = 1 << (h - len_ - 1)rot = 1for 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_moda[i + offset] = (l + r) % _fft_moda[i + offset + p] = (l - r) % _fft_modif s + 1 != (1 << len_):rot *= _fft_rate2[(~s & -~s).bit_length() - 1]rot %= _fft_modlen_ += 1else:p = 1 << (h - len_ - 2)rot = 1for s in range(1 << len_):rot2 = rot * rot % _fft_modrot3 = rot2 * rot % _fft_modoffset = s << (h - len_)for i in range(p):a0 = a[i + offset]a1 = a[i + offset + p] * rota2 = a[i + offset + p * 2] * rot2a3 = a[i + offset + p * 3] * rot3a1na3imag = (a1 - a3) % _fft_mod * _fft_imaga[i + offset] = (a0 + a2 + a1 + a3) % _fft_moda[i + offset + p] = (a0 + a2 - a1 - a3) % _fft_moda[i + offset + p * 2] = (a0 - a2 + a1na3imag) % _fft_moda[i + offset + p * 3] = (a0 - a2 - a1na3imag) % _fft_modif s + 1 != (1 << len_):rot *= _fft_rate3[(~s & -~s).bit_length() - 1]rot %= _fft_modlen_ += 2def _butterfly_inv(a):n = len(a)h = (n - 1).bit_length()len_ = hwhile len_:if len_ == 1:p = 1 << (h - len_)irot = 1for 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_moda[i + offset + p] = (l - r) * irot % _fft_modif s + 1 != (1 << (len_ - 1)):irot *= _fft_irate2[(~s & -~s).bit_length() - 1]irot %= _fft_modlen_ -= 1else:p = 1 << (h - len_)irot = 1for s in range(1 << (len_ - 2)):irot2 = irot * irot % _fft_modirot3 = irot2 * irot % _fft_modoffset = 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_moda[i + offset] = (a0 + a1 + a2 + a3) % _fft_moda[i + offset + p] = (a0 - a1 +a2na3iimag) * irot % _fft_moda[i + offset + p * 2] = (a0 + a1 -a2 - a3) * irot2 % _fft_moda[i + offset + p * 3] = (a0 - a1 -a2na3iimag) * irot3 % _fft_modif s + 1 != (1 << (len_ - 1)):irot *= _fft_irate3[(~s & -~s).bit_length() - 1]irot %= _fft_modlen_ -= 2def _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_modelse:for i in range(n):for j in range(m):ans[i + j] = (ans[i + j] + a[i] * b[j]) % _fft_modreturn ansdef _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_modreturn adef _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_modreturn adef 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) <= 8388609Complexity----------> 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 = 1for i in range(1,len(f)):t = t * a % mode[i] = e[i] * t % modres = 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()-1f = 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) % modres = convolve(res,h,2**i)return res[:limit]import sys,random,bisectfrom collections import deque,defaultdictfrom heapq import heapify,heappop,heappushfrom itertools import permutationsfrom math import log,gcdinput = 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 0return g1[n] * (g2[n-r] * g2[r] % mod) % modN = 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) % modX = [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) % modif 2*i+q <= 2*N:Y[2*i+q] = (g2[i] * g2[i+q] % mod) * pow(y,2*i+q,mod) % modXY = convolve(X,Y,2*N+1)f = [0] * (N+1)for i in range(N+1):f[i] = XY[2*i] * g1[2*i] % modp,q = 0,0X = [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) % modif 2*i+q <= 2*N:Y[2*i+q] = (g2[i] * g2[i+q] % mod) * pow(y,2*i+q,mod) % modXY = convolve(X,Y,2*N+1)g = [0] * (N+1)for i in range(N+1):g[i] = XY[2*i] * g1[2*i] % modig = inverse(g,N+1)h = convolve(f,ig,N+1)res = 0for i in range(N):res += h[i+1] * P[i]res %= modprint(res)