結果

問題 No.2770 Coupon Optimization
ユーザー mkawa2mkawa2
提出日時 2024-05-31 23:07:05
言語 PyPy3
(7.3.15)
結果
AC  
実行時間 816 ms / 3,000 ms
コード長 13,070 bytes
コンパイル時間 284 ms
コンパイル使用メモリ 82,424 KB
実行使用メモリ 168,992 KB
最終ジャッジ日時 2024-05-31 23:07:18
合計ジャッジ時間 11,748 ms
ジャッジサーバーID
(参考情報)
judge4 / judge3
このコードへのチャレンジ
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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 44 ms
55,912 KB
testcase_01 AC 41 ms
56,592 KB
testcase_02 AC 42 ms
56,416 KB
testcase_03 AC 732 ms
166,380 KB
testcase_04 AC 721 ms
168,992 KB
testcase_05 AC 79 ms
102,612 KB
testcase_06 AC 757 ms
165,712 KB
testcase_07 AC 771 ms
160,432 KB
testcase_08 AC 801 ms
166,036 KB
testcase_09 AC 352 ms
95,920 KB
testcase_10 AC 456 ms
117,828 KB
testcase_11 AC 442 ms
108,780 KB
testcase_12 AC 484 ms
125,096 KB
testcase_13 AC 457 ms
117,172 KB
testcase_14 AC 804 ms
165,628 KB
testcase_15 AC 816 ms
166,896 KB
testcase_16 AC 787 ms
165,840 KB
testcase_17 AC 806 ms
165,820 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 #

import sys

# sys.setrecursionlimit(1000006)
# sys.set_int_max_str_digits(200005)
int1 = lambda x: int(x)-1
pDB = 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-(-1 << 31)
inf = -1-(-1 << 62)

# md = 10**9+7
md = 998244353

imag = 911660635
iimag = 86583718
rate2 = (
911660635, 509520358, 369330050, 332049552, 983190778, 123842337, 238493703, 975955924, 603855026, 856644456, 131300601,
842657263, 730768835, 942482514, 806263778, 151565301, 510815449, 503497456, 743006876, 741047443, 56250497, 867605899)
irate2 = (
86583718, 372528824, 373294451, 645684063, 112220581, 692852209, 155456985, 797128860, 90816748, 860285882, 927414960,
354738543, 109331171, 293255632, 535113200, 308540755, 121186627, 608385704, 438932459, 359477183, 824071951, 103369235)
rate3 = (
372528824, 337190230, 454590761, 816400692, 578227951, 180142363, 83780245, 6597683, 70046822, 623238099, 183021267,
402682409, 631680428, 344509872, 689220186, 365017329, 774342554, 729444058, 102986190, 128751033, 395565204)
irate3 = (
509520358, 929031873, 170256584, 839780419, 282974284, 395914482, 444904435, 72135471, 638914820, 66769500, 771127074,
985925487, 262319669, 262341272, 625870173, 768022760, 859816005, 914661783, 430819711, 272774365, 530924681)

def Tonelli_Shanks(N, p):
    if pow(N, p >> 1, p) == p-1:
        retu = None
    elif p%4 == 3:
        retu = pow(N, (p+1)//4, p)
    else:
        for nonresidue in range(1, p):
            if pow(nonresidue, p >> 1, p) == p-1:
                break
        pp = p-1
        cnt = 0
        while pp%2 == 0:
            pp //= 2
            cnt += 1
        s = pow(N, pp, p)
        retu = pow(N, (pp+1)//2, p)
        for i in range(cnt-2, -1, -1):
            if pow(s, 1 << i, p) == p-1:
                s *= pow(nonresidue, p >> 1+i, p)
                s %= p
                retu *= pow(nonresidue, p >> 2+i, p)
                retu %= p
    return retu

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%md
                    a[i+offset] = (l+r)%md
                    a[i+offset+p] = (l-r)%md
                if s+1 != 1 << len_:
                    rot *= rate2[(~s & -~s).bit_length()-1]
                    rot %= md
            len_ += 1
        else:
            p = 1 << (h-len_-2)
            rot = 1
            for s in range(1 << len_):
                rot2 = rot*rot%md
                rot3 = rot2*rot%md
                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)%md*imag
                    a[i+offset] = (a0+a2+a1+a3)%md
                    a[i+offset+p] = (a0+a2-a1-a3)%md
                    a[i+offset+p*2] = (a0-a2+a1na3imag)%md
                    a[i+offset+p*3] = (a0-a2-a1na3imag)%md
                if s+1 != 1 << len_:
                    rot *= rate3[(~s & -~s).bit_length()-1]
                    rot %= md
            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)%md
                    a[i+offset+p] = (l-r)*irot%md
                if s+1 != (1 << (len_-1)):
                    irot *= irate2[(~s & -~s).bit_length()-1]
                    irot %= md
            len_ -= 1
        else:
            p = 1 << (h-len_)
            irot = 1
            for s in range(1 << (len_-2)):
                irot2 = irot*irot%md
                irot3 = irot2*irot%md
                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)*iimag%md
                    a[i+offset] = (a0+a1+a2+a3)%md
                    a[i+offset+p] = (a0-a1+a2na3iimag)*irot%md
                    a[i+offset+p*2] = (a0+a1-a2-a3)*irot2%md
                    a[i+offset+p*3] = (a0-a1-a2na3iimag)*irot3%md
                if s+1 != (1 << (len_-2)):
                    irot *= irate3[(~s & -~s).bit_length()-1]
                    irot %= md
            len_ -= 2

def integrate(a):
    a = a.copy()
    n = len(a)
    assert n > 0
    a.pop()
    a.insert(0, 0)
    inv = [1, 1]
    for i in range(2, n):
        inv.append(-inv[md%i]*(md//i)%md)
        a[i] = a[i]*inv[i]%md
    return a

def differentiate(a):
    n = len(a)
    assert n > 0
    for i in range(2, n):
        a[i] = a[i]*i%md
    a.pop(0)
    a.append(0)
    return a

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])%md
    else:
        for i in range(n):
            for j in range(m):
                ans[i+j] = (ans[i+j]+a[i]*b[j])%md
    return ans

def convolution_ntt(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]%md
    butterfly_inv(a)
    a = a[:n+m-1]
    iz = pow(z, md-2, md)
    for i in range(n+m-1):
        a[i] = a[i]*iz%md
    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]%md
    butterfly_inv(a)
    a = a[:2*n-1]
    iz = pow(z, md-2, md)
    for i in range(2*n-1):
        a[i] = a[i]*iz%md
    return a

def convolution(a, b):
    """It calculates (+, x) convolution in md 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.

    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) <= 60:
        return convolution_naive(a, b)
    if a is b:
        return convolution_square(a)
    return convolution_ntt(a, b)

def inverse(a):
    n = len(a)
    assert n > 0 and a[0] != 0
    res = [pow(a[0], md-2, md)]
    m = 1
    while m < n:
        f = a[:min(n, 2*m)]+[0]*(2*m-min(n, 2*m))
        g = res+[0]*m
        butterfly(f)
        butterfly(g)
        for i in range(2*m):
            f[i] = f[i]*g[i]%md
        butterfly_inv(f)
        f = f[m:]+[0]*m
        butterfly(f)
        for i in range(2*m):
            f[i] = f[i]*g[i]%md
        butterfly_inv(f)
        iz = pow(2*m, md-2, md)
        iz = (-iz*iz)%md
        for i in range(m):
            f[i] = f[i]*iz%md
        res += f[:m]
        m <<= 1
    return res[:n]

def log(a):
    a = a.copy()
    n = len(a)
    assert n > 0 and a[0] == 1
    a_inv = inverse(a)
    a = differentiate(a)
    a = convolution(a, a_inv)[:n]
    a = integrate(a)
    return a

def exp(a):
    a = a.copy()
    n = len(a)
    assert n > 0 and a[0] == 0
    g = [1]
    a[0] = 1
    h_drv = a.copy()
    h_drv = differentiate(h_drv)
    m = 1
    while m < n:
        f_fft = a[:m]+[0]*m
        butterfly(f_fft)

        if m > 1:
            _f = [f_fft[i]*g_fft[i]%md for i in range(m)]
            butterfly_inv(_f)
            _f = _f[m//2:]+[0]*(m//2)
            butterfly(_f)
            for i in range(m):
                _f[i] = _f[i]*g_fft[i]%md
            butterfly_inv(_f)
            _f = _f[:m//2]
            iz = pow(m, md-2, md)
            iz *= -iz
            iz %= md
            for i in range(m//2):
                _f[i] = _f[i]*iz%md
            g.extend(_f)

        t = a[:m]
        t = differentiate(t)
        r = h_drv[:m-1]
        r.append(0)
        butterfly(r)
        for i in range(m):
            r[i] = r[i]*f_fft[i]%md
        butterfly_inv(r)
        im = pow(-m, md-2, md)
        for i in range(m):
            r[i] = r[i]*im%md
        for i in range(m):
            t[i] = (t[i]+r[i])%md
        t = [t[-1]]+t[:-1]

        t += [0]*m
        butterfly(t)
        g_fft = g+[0]*(2*m-len(g))
        butterfly(g_fft)
        for i in range(2*m):
            t[i] = t[i]*g_fft[i]%md
        butterfly_inv(t)
        t = t[:m]
        i2m = pow(2*m, md-2, md)
        for i in range(m):
            t[i] = t[i]*i2m%md

        v = a[m:min(n, 2*m)]
        v += [0]*(m-len(v))
        t = [0]*(m-1)+t+[0]
        t = integrate(t)
        for i in range(m):
            v[i] = (v[i]-t[m+i])%md

        v += [0]*m
        butterfly(v)
        for i in range(2*m):
            v[i] = v[i]*f_fft[i]%md
        butterfly_inv(v)
        v = v[:m]
        i2m = pow(2*m, md-2, md)
        for i in range(m):
            v[i] = v[i]*i2m%md

        for i in range(min(n-m, m)):
            a[m+i] = v[i]

        m *= 2
    return a

def power(a, k):
    n = len(a)
    assert n > 0
    if k == 0:
        return [1]+[0]*(n-1)
    l = 0
    while l < len(a) and not a[l]:
        l += 1
    if l*k >= n:
        return [0]*n
    ic = pow(a[l], md-2, md)
    pc = pow(a[l], k, md)
    a = log([a[i]*ic%md for i in range(l, len(a))])
    for i in range(len(a)):
        a[i] = a[i]*k%md
    a = exp(a)
    for i in range(len(a)):
        a[i] = a[i]*pc%md
    a = [0]*(l*k)+a[:n-l*k]
    return a

def sqrt(a):
    if len(a) == 0:
        return []
    if a[0] == 0:
        for d in range(1, len(a)):
            if a[d]:
                if d & 1:
                    return None
                if len(a)-1 < d//2:
                    break
                res = sqrt(a[d:]+[0]*(d//2))
                if res == None:
                    return None
                res = [0]*(d//2)+res
                return res
        return [0]*len(a)

    sqr = Tonelli_Shanks(a[0], md)
    if sqr == None:
        return None
    T = [0]*(len(a))
    T[0] = sqr
    res = T.copy()
    T[0] = pow(sqr, md-2, md)  # T:res^{-1}
    m = 1
    two_inv = (md+1)//2
    F = [sqr]
    while m <= len(a)-1:
        for i in range(m):
            F[i] *= F[i]
            F[i] %= md
        butterfly_inv(F)
        iz = pow(m, md-2, md)
        for i in range(m):
            F[i] = F[i]*iz%md
        delta = [0]*(2*m)
        for i in range(m):
            delta[i+m] = F[i]-a[i]-(a[i+m] if i+m < len(a) else 0)
        butterfly(delta)
        G = [0]*(2*m)
        for i in range(m):
            G[i] = T[i]
        butterfly(G)
        for i in range(2*m):
            delta[i] *= G[i]
            delta[i] %= md
        butterfly_inv(delta)
        iz = pow(2*m, md-2, md)
        for i in range(2*m):
            delta[i] = delta[i]*iz%md
        for i in range(m, min(2*m, len(a))):
            res[i] = -delta[i]*two_inv%md
            res[i] %= md
        if 2*m > len(a)-1:
            break
        F = res[:2*m]
        butterfly(F)
        eps = [F[i]*G[i]%md for i in range(2*m)]
        butterfly_inv(eps)
        for i in range(m):
            eps[i] = 0
        iz = pow(2*m, md-2, md)
        for i in range(m, 2*m):
            eps[i] = eps[i]*iz%md
        butterfly(eps)
        for i in range(2*m):
            eps[i] *= G[i]
            eps[i] %= md
        butterfly_inv(eps)
        for i in range(m, 2*m):
            T[i] = -eps[i]*iz
            T[i] %= md
        iz = iz*iz%md

        m <<= 1
    return res

n,m=LI()
aa=LI()
bb=LI()

aa.sort()
aa=[a//100 for a in aa]
a1=[a//1000000 for a in aa]
a2=[a//10000%100 for a in aa]
a3=[a//100%100 for a in aa]
a4=[a%100 for a in aa]
# pDB(al,ar)

bb=[100-b for b in bb]
bb.sort()
bb=bb[:n]
if m<n:bb+=[100]*(n-m)
# pDB(aa,bb)
c1=convolution(a1,bb)[:n]
c2=convolution(a2,bb)[:n]
c3=convolution(a3,bb)[:n]
c4=convolution(a4,bb)[:n]
for a,b,c,d in zip(c1,c2,c3,c4):
    print(a*1000000+b*10000+c*100+d)
0