結果
問題 | No.2770 Coupon Optimization |
ユーザー |
👑 |
提出日時 | 2024-05-31 22:08:14 |
言語 | PyPy3 (7.3.15) |
結果 |
AC
|
実行時間 | 864 ms / 3,000 ms |
コード長 | 12,710 bytes |
コンパイル時間 | 288 ms |
コンパイル使用メモリ | 82,668 KB |
実行使用メモリ | 151,844 KB |
最終ジャッジ日時 | 2024-12-20 23:39:55 |
合計ジャッジ時間 | 12,852 ms |
ジャッジサーバーID (参考情報) |
judge3 / judge2 |
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ファイルパターン | 結果 |
---|---|
sample | AC * 2 |
other | AC * 16 |
ソースコード
class NTT998:# fmt: offrate2=(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)# fmt: ondef 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) % 998244353A[i + offset + p] = (l - r) % 998244353rot *= NTT998.rate2[(~s & -~s).bit_length()]rot %= 998244353le += 1else:p = 1 << (h - le - 2)rot = 1for s in range(1 << le):rot2 = rot * rot % 998244353rot3 = rot2 * rot % 998244353offset = 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) % 998244353 * 911660635A[i + offset] = (a0 + a2 + a1 + a3) % 998244353A[i + offset + p] = (a0 + a2 - a1 - a3) % 998244353A[i + offset + p * 2] = (a0 - a2 + a1na3imag) % 998244353A[i + offset + p * 3] = (a0 - a2 - a1na3imag) % 998244353rot *= NTT998.rate3[(~s & -~s).bit_length()]rot %= 998244353le += 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) % 998244353A[i + offset + p] = (l - r) * irot % 998244353irot *= NTT998.irate2[(~s & -~s).bit_length()]irot %= 998244353le -= 1else:p = 1 << (h - le)irot = 1for s in range(1 << (le - 2)):irot2 = irot * irot % 998244353irot3 = irot2 * irot % 998244353offset = 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) * 86583718 % 998244353A[i + offset] = (a0 + a1 + a2 + a3) % 998244353A[i + offset + p] = (a0 - a1 + a2na3iimag) * irot % 998244353A[i + offset + p * 2] = (a0 + a1 - a2 - a3) * irot2 % 998244353A[i + offset + p * 3] = ((a0 - a1 - a2na3iimag) * irot3 % 998244353)irot *= NTT998.irate3[(~s & -~s).bit_length()]irot %= 998244353le -= 2def multiply(A, B):n = len(A)m = len(B)if min(n, m) <= 60:C = [0] * (n + m - 1)for i in range(n):if i % 8 == 0:for j in range(m):C[i + j] += A[i] * B[j]C[i + j] %= 998244353else:for j in range(m):C[i + j] += A[i] * B[j]return [c % 998244353 for c in C]A = A[:]B = B[:]z = 1 << (n + m - 2).bit_length()A += [0] * (z - n)B += [0] * (z - m)NTT998.butterfly(A)NTT998.butterfly(B)for i in range(z):A[i] *= B[i]A[i] %= 998244353NTT998.butterfly_inv(A)A = A[: n + m - 1]iz = pow(z, 998244353 - 2, 998244353)return [a * iz % 998244353 for a in A]class NTT:def __init__(self, MOD=998244353):self.MOD = MODself.make_info(MOD)def make_info(self, MOD):g = self.primitive_root(MOD)m = MOD - 1rank2 = (m & -m).bit_length() - 1root = [0] * (rank2 + 1)iroot = [0] * (rank2 + 1)rate2 = [0] * (rank2 + 1)irate2 = [0] * (rank2 + 1)rate3 = [0] * (rank2)irate3 = [0] * (rank2)root[rank2] = pow(g, (MOD - 1) >> rank2, MOD)iroot[rank2] = pow(root[rank2], MOD - 2, MOD)for i in range(rank2 - 1, -1, -1):root[i] = root[i + 1] * root[i + 1] % MODiroot[i] = iroot[i + 1] * iroot[i + 1] % MODprod = 1iprod = 1for i in range(1, rank2):rate2[i] = root[i + 1] * prod % MODirate2[i] = iroot[i + 1] * iprod % MODprod = prod * iroot[i + 1] % MODiprod = iprod * root[i + 1] % MODprod = 1iprod = 1for i in range(1, rank2 - 1):rate3[i] = root[i + 2] * prod % MODirate3[i] = iroot[i + 2] * iprod % MODprod = prod * iroot[i + 2] % MODiprod = iprod * root[i + 2] % MODself.IMAG = rate2[1]self.IIMAG = irate2[1]self.rate2 = rate2self.irate2 = irate2self.rate3 = rate3self.irate3 = irate3def primitive_root(self, MOD):if MOD == 998244353:return 3elif MOD == 200003:return 2elif MOD == 167772161:return 3elif MOD == 469762049:return 3elif MOD == 754974721:return 11divs = [0] * 20divs[0] = 2cnt = 1x = (MOD - 1) // 2while x % 2 == 0:x //= 2i = 3while i * i <= x:if x % i == 0:divs[cnt] = icnt += 1while x % i == 0:x //= ii += 2if x > 1:divs[cnt] = xcnt += 1g = 2while 1:ok = Truefor i in range(cnt):if pow(g, (MOD - 1) // divs[i], MOD) == 1:ok = Falsebreakif ok:return gg += 1def butterfly(self, 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) % self.MODA[i + offset + p] = (l - r) % self.MODrot *= self.rate2[(~s & -~s).bit_length()]rot %= self.MODle += 1else:p = 1 << (h - le - 2)rot = 1for s in range(1 << le):rot2 = rot * rot % self.MODrot3 = rot2 * rot % self.MODoffset = 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) % self.MOD * self.IMAGA[i + offset] = (a0 + a2 + a1 + a3) % self.MODA[i + offset + p] = (a0 + a2 - a1 - a3) % self.MODA[i + offset + p * 2] = (a0 - a2 + a1na3imag) % self.MODA[i + offset + p * 3] = (a0 - a2 - a1na3imag) % self.MODrot *= self.rate3[(~s & -~s).bit_length()]rot %= self.MODle += 2def butterfly_inv(self, 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) % self.MODA[i + offset + p] = (l - r) * irot % self.MODirot *= self.irate2[(~s & -~s).bit_length()]irot %= self.MODle -= 1else:p = 1 << (h - le)irot = 1for s in range(1 << (le - 2)):irot2 = irot * irot % self.MODirot3 = irot2 * irot % self.MODoffset = 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) * self.IIMAG % self.MODA[i + offset] = (a0 + a1 + a2 + a3) % self.MODA[i + offset + p] = (a0 - a1 + a2na3iimag) * irot % self.MODA[i + offset + p * 2] = (a0 + a1 - a2 - a3) * irot2 % self.MODA[i + offset + p * 3] = ((a0 - a1 - a2na3iimag) * irot3 % self.MOD)irot *= self.irate3[(~s & -~s).bit_length()]irot %= self.MODle -= 2def multiply(self, A, B):n = len(A)m = len(B)if min(n, m) <= 60:C = [0] * (n + m - 1)for i in range(n):if i % 8 == 0:for j in range(m):C[i + j] += A[i] * B[j]C[i + j] %= self.MODelse:for j in range(m):C[i + j] += A[i] * B[j]return [c % self.MOD for c in C]A = A[:]B = B[:]z = 1 << (n + m - 2).bit_length()A += [0] * (z - n)B += [0] * (z - m)self.butterfly(A)self.butterfly(B)for i in range(z):A[i] *= B[i]A[i] %= self.MODself.butterfly_inv(A)A = A[: n + m - 1]iz = pow(z, self.MOD - 2, self.MOD)return [a * iz % self.MOD for a in A]MOD = 998244353n, m = map(int, input().split())A = list(map(int, input().split()))B = list(map(int, input().split()))A.sort()B.sort(reverse=True)B += [0] * (n - m)inv100 = pow(100, -1, MOD)B2 = B[:]for i in range(n):B2[i] = (100 - B2[i]) * inv100 % MODC = NTT998.multiply(A, B2)MOD2 = 924844033B2 = B[:]inv100 = pow(100, -1, MOD2)for i in range(n):B2[i] = (100 - B2[i]) * inv100 % MOD2C2 = NTT(MOD2).multiply(A, B2)ans = []times = pow(MOD, -1, MOD2)for c, c2 in zip(C[:n], C2[:n]):x = (c2 - c) * times % MOD2r = c + MOD * xans.append(r)print(*ans, sep="\n")