結果
問題 | No.931 Multiplicative Convolution |
ユーザー |
![]() |
提出日時 | 2023-03-17 18:40:58 |
言語 | PyPy3 (7.3.15) |
結果 |
AC
|
実行時間 | 238 ms / 2,000 ms |
コード長 | 5,988 bytes |
コンパイル時間 | 155 ms |
コンパイル使用メモリ | 82,440 KB |
実行使用メモリ | 135,304 KB |
最終ジャッジ日時 | 2024-09-18 10:06:30 |
合計ジャッジ時間 | 4,611 ms |
ジャッジサーバーID (参考情報) |
judge1 / judge3 |
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ファイルパターン | 結果 |
---|---|
sample | AC * 3 |
other | AC * 14 |
ソースコード
import sys# sys.setrecursionlimit(200005)int1 = lambda x: int(x)-1pDB = lambda *x: print(*x, end="\n", file=sys.stderr)p2D = lambda x: print(*x, sep="\n", end="\n\n", file=sys.stderr)def II(): return int(sys.stdin.readline())def LI(): return list(map(int, sys.stdin.readline().split()))def LLI(rows_number): return [LI() for _ in range(rows_number)]def LI1(): return list(map(int1, sys.stdin.readline().split()))def LLI1(rows_number): return [LI1() for _ in range(rows_number)]def SI(): return sys.stdin.readline().rstrip()dij = [(0, 1), (-1, 0), (0, -1), (1, 0)]# dij = [(0, 1), (-1, 0), (0, -1), (1, 0), (1, 1), (1, -1), (-1, 1), (-1, -1)]inf = (1 << 63)-1# inf = (1 << 31)-1# md = 10**9+7md = 998244353IMAG = 911660635IIMAG = 86583718rate2 = (0, 911660635, 509520358, 369330050, 332049552, 983190778, 123842337, 238493703, 975955924, 603855026, 856644456,131300601, 842657263, 730768835, 942482514, 806263778, 151565301, 510815449, 503497456, 743006876, 741047443,56250497,867605899, 0)irate2 = (0, 86583718, 372528824, 373294451, 645684063, 112220581, 692852209, 155456985, 797128860, 90816748, 860285882,927414960, 354738543, 109331171, 293255632, 535113200, 308540755, 121186627, 608385704, 438932459, 359477183,824071951, 103369235, 0)rate3 = (0, 372528824, 337190230, 454590761, 816400692, 578227951, 180142363, 83780245, 6597683, 70046822, 623238099,183021267,402682409, 631680428, 344509872, 689220186, 365017329, 774342554, 729444058, 102986190, 128751033, 395565204, 0)irate3 = (0, 509520358, 929031873, 170256584, 839780419, 282974284, 395914482, 444904435, 72135471, 638914820, 66769500,771127074, 985925487, 262319669, 262341272, 625870173, 768022760, 859816005, 914661783, 430819711, 272774365,530924681, 0)def butterfly(a):n = len(a)h = (n-1).bit_length()le = 0while le < h:if h-le == 1:p = 1 << (h-le-1)rot = 1for s in range(1 << le):offset = s << (h-le)for i in range(p):l = a[i+offset]r = a[i+offset+p]*rota[i+offset] = (l+r)%mda[i+offset+p] = (l-r)%mdrot *= rate2[(~s & -~s).bit_length()]rot %= mdle += 1else:p = 1 << (h-le-2)rot = 1for s in range(1 << le):rot2 = rot*rot%mdrot3 = rot2*rot%mdoffset = s << (h-le)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)%md*IMAGa[i+offset] = (a0+a2+a1+a3)%mda[i+offset+p] = (a0+a2-a1-a3)%mda[i+offset+p*2] = (a0-a2+a1na3imag)%mda[i+offset+p*3] = (a0-a2-a1na3imag)%mdrot *= rate3[(~s & -~s).bit_length()]rot %= mdle += 2def butterfly_inv(a):n = len(a)h = (n-1).bit_length()le = hwhile le:if le == 1:p = 1 << (h-le)irot = 1for s in range(1 << (le-1)):offset = s << (h-le+1)for i in range(p):l = a[i+offset]r = a[i+offset+p]a[i+offset] = (l+r)%mda[i+offset+p] = (l-r)*irot%mdirot *= irate2[(~s & -~s).bit_length()]irot %= mdle -= 1else:p = 1 << (h-le)irot = 1for s in range(1 << (le-2)):irot2 = irot*irot%mdirot3 = irot2*irot%mdoffset = s << (h-le+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)*IIMAG%mda[i+offset] = (a0+a1+a2+a3)%mda[i+offset+p] = (a0-a1+a2na3iimag)*irot%mda[i+offset+p*2] = (a0+a1-a2-a3)*irot2%mda[i+offset+p*3] = (a0-a1-a2na3iimag)*irot3%mdirot *= irate3[(~s & -~s).bit_length()]irot %= mdle -= 2def multiply(s, t):n = len(s)m = len(t)if min(n, m) <= 60:a = [0]*(n+m-1)for i in range(n):if i%8 == 0:for j in range(m):a[i+j] += s[i]*t[j]a[i+j] %= mdelse:for j in range(m):a[i+j] += s[i]*t[j]return [x%md for x in a]a = s.copy()b = t.copy()z = 1 << (n+m-2).bit_length()a += [0]*(z-n)b += [0]*(z-m)butterfly(a)butterfly(b)for i in range(z):a[i] *= b[i]a[i] %= mdbutterfly_inv(a)a = a[:n+m-1]iz = pow(z, md-2, md)return [v*iz%md for v in a]def find_primitive_root(p):def is_primitive_root(r):atoe = [-1]*pa = 1for e in range(p-1):if atoe[a] != -1: return Noneatoe[a] = ea = a*r%preturn atoefor r in range(2, p):atoe = is_primitive_root(r)if atoe: return atoereturn Nonep = II()aa = LI()bb = LI()if p == 2:print(aa[0]*bb[0]%md)exit()itoe = find_primitive_root(p)etoi = [-1]*pfor i, e in enumerate(itoe[1:], 1): etoi[e] = idef toxx(aa):xx = [0]*pfor i, a in enumerate(aa, 1):e = itoe[i]xx[e] += areturn xxxx = toxx(aa)yy = toxx(bb)cc = multiply(xx, yy)# print(cc)ans = [0]*pfor e, c in enumerate(cc):i = etoi[e%(p-1)]ans[i] += cans[i] %= mdprint(*ans[1:])