結果

問題 No.2966 Simple Plus Minus Problem
ユーザー 遭難者
提出日時 2024-10-29 15:39:56
言語 PyPy3
(7.3.15)
結果
AC  
実行時間 1,115 ms / 2,567 ms
コード長 11,902 bytes
コンパイル時間 393 ms
コンパイル使用メモリ 82,584 KB
実行使用メモリ 163,912 KB
最終ジャッジ日時 2024-10-30 08:24:12
合計ジャッジ時間 31,165 ms
ジャッジサーバーID
（参考情報） 		judge2 / judge4
このコードへのチャレンジ
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ファイルパターン 結果
sample AC * 3
other AC * 54
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 #
プレゼンテーションモードにする

from atexit import register
from os import read, write
import sys
MOD = 998244353
_IMAG = 911660635
_IIMAG = 86583718
_rate2 = (
    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 _fft(a):
    n = len(a)
    h = (n - 1).bit_length()
    le = 0
    for le in range(0, h - 1, 2):
        p = 1 << (h - le - 2)
        rot = 1
        for s in range(1 << le):
            rot2 = rot * rot % MOD
            rot3 = rot2 * rot % MOD
            offset = s << (h - le)
            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) % MOD * _IMAG
                a[i + offset] = (a0 + a2 + a1 + a3) % MOD
                a[i + offset + p] = (a0 + a2 - a1 - a3) % MOD
                a[i + offset + p * 2] = (a0 - a2 + a1na3imag) % MOD
                a[i + offset + p * 3] = (a0 - a2 - a1na3imag) % MOD
            rot = rot * _rate3[(~s & -~s).bit_length()] % MOD
    if h - le & 1:
        rot = 1
        for s in range(1 << (h - 1)):
            offset = s << 1
            l = a[offset]
            r = a[offset + 1] * rot
            a[offset] = (l + r) % MOD
            a[offset + 1] = (l - r) % MOD
            rot = rot * _rate2[(~s & -~s).bit_length()] % MOD
def _ifft(a):
    n = len(a)
    h = (n - 1).bit_length()
    le = h
    for le in range(h, 1, -2):
        p = 1 << (h - le)
        irot = 1
        for s in range(1 << (le - 2)):
            irot2 = irot * irot % MOD
            irot3 = irot2 * irot % MOD
            offset = 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 % MOD
                a[i + offset] = (a0 + a1 + a2 + a3) % MOD
                a[i + offset + p] = (a0 - a1 + a2na3iimag) * irot % MOD
                a[i + offset + p * 2] = (a0 + a1 - a2 - a3) * irot2 % MOD
                a[i + offset + p * 3] = (a0 - a1 - a2na3iimag) * irot3 % MOD
            irot = irot * _irate3[(~s & -~s).bit_length()] % MOD
    if le & 1:
        p = 1 << (h - 1)
        for i in range(p):
            l = a[i]
            r = a[i + p]
            a[i] = l + r if l + r < MOD else l + r - MOD
            a[i + p] = l - r if l - r >= 0 else l - r + MOD
def ntt(a) -> None:
    if len(a) <= 1:
        return
    _fft(a)
def intt(a) -> None:
    if len(a) <= 1:
        return
    _ifft(a)
    iv = pow(len(a), MOD - 2, MOD)
    for i, x in enumerate(a):
        a[i] = x * iv % MOD
def multiply(s: list, t: list) -> list:
    n, m = len(s), len(t)
    l = n + m - 1
    if min(n, m) <= 60:
        a = [0] * l
        for i, x in enumerate(s):
            for j, y in enumerate(t):
                a[i + j] += x * y
        return [x % MOD for x in a]
    z = 1 << (l - 1).bit_length()
    a = s + [0] * (z - n)
    b = t + [0] * (z - m)
    _fft(a)
    _fft(b)
    for i, x in enumerate(b):
        a[i] = a[i] * x % MOD
    _ifft(a)
    a[l:] = []
    iz = pow(z, MOD - 2, MOD)
    return [x * iz % MOD for x in a]
def pow2(s: list) -> list:
    n = len(s)
    l = (n << 1) - 1
    if n <= 60:
        a = [0] * l
        for i, x in enumerate(s):
            for j, y in enumerate(s):
                a[i + j] += x * y
        return [x % MOD for x in a]
    z = 1 << (l - 1).bit_length()
    a = s + [0] * (z - n)
    _fft(a)
    for i, x in enumerate(a):
        a[i] = x * x % MOD
    _ifft(a)
    a[l:] = []
    iz = pow(z, MOD - 2, MOD)
    return [x * iz % MOD for x in a]
def ntt_doubling(a: list) -> None:
    M = len(a)
    b = a[:]
    intt(b)
    r = 1
    zeta = pow(3, (MOD - 1) // (M << 1), MOD)
    for i, x in enumerate(b):
        b[i] = x * r % MOD
        r = r * zeta % MOD
    ntt(b)
    a += b
# https://nyaannyaan.github.io/library/fps/formal-power-series.hpp
def shrink(a: list) -> None:
    while a and not a[-1]:
        a.pop()
def fps_add(a: list, b: list) -> list:
    if len(a) < len(b):
        res = b[::]
        for i, x in enumerate(a):
            res[i] += x
    else:
        res = a[::]
        for i, x in enumerate(b):
            res[i] += x
    return [x % MOD for x in res]
def fps_add_scalar(a: list, k: int) -> list:
    res = a[:]
    res[0] = (res[0] + k) % MOD
    return res
def fps_sub(a: list, b: list) -> list:
    if len(a) < len(b):
        res = b[::]
        for i, x in enumerate(a):
            res[i] -= x
        res = fps_neg(res)
    else:
        res = a[::]
        for i, x in enumerate(b):
            res[i] -= x
    return [x % MOD for x in res]
def fps_sub_scalar(a: list, k: int) -> list:
    return fps_add_scalar(a, -k)
def fps_neg(a: list) -> list:
    return [MOD - x if x else 0 for x in a]
def fps_mul_scalar(a: list, k: int) -> list:
    return [x * k % MOD for x in a]
def fps_matmul(a: list, b: list) -> list:
    "not verified"
    return [x * b[i] % MOD for i, x in enumerate(a)]
def fps_div(a: list, b: list) -> list:
    if len(a) < len(b):
        return []
    n = len(a) - len(b) + 1
    cnt = 0
    if len(b) > 64:
        return multiply(a[::-1][:n], fps_inv(b[::-1], n))[:n][::-1]
    f, g = a[::], b[::]
    while g and not g[-1]:
        g.pop()
        cnt += 1
    coef = pow(g[-1], MOD - 2, MOD)
    g = fps_mul_scalar(g, coef)
    deg = len(f) - len(g) + 1
    gs = len(g)
    quo = [0] * deg
    for i in range(deg)[::-1]:
        quo[i] = x = f[i + gs - 1] % MOD
        for j, y in enumerate(g):
            f[i + j] -= x * y
    return fps_mul_scalar(quo, coef) + [0] * cnt
def fps_mod(a: list, b: list) -> list:
    res = fps_sub(a, multiply(fps_div(a, b), b))
    while res and not res[-1]:
        res.pop()
    return res
def fps_divmod(a: list, b: list):
    q = fps_div(a, b)
    r = fps_sub(a, multiply(q, b))
    while r and not r[-1]:
        r.pop()
    return q, r
def fps_eval(a: list, x: int) -> int:
    r = 0
    w = 1
    for v in a:
        r += w * v % MOD
        w = w * x % MOD
    return r % MOD
def fps_inv(a: list, deg: int = -1) -> list:
    # assert(self[0] != 0)
    if deg == -1:
        deg = len(a)
    res = [0] * deg
    res[0] = pow(a[0], MOD - 2, MOD)
    d = 1
    while d < deg:
        f = [0] * (d << 1)
        tmp = min(len(a), d << 1)
        f[:tmp] = a[:tmp]
        g = [0] * (d << 1)
        g[:d] = res[:d]
        ntt(f)
        ntt(g)
        for i, x in enumerate(g):
            f[i] = f[i] * x % MOD
        intt(f)
        f[:d] = [0] * d
        ntt(f)
        for i, x in enumerate(g):
            f[i] = f[i] * x % MOD
        intt(f)
        for j in range(d, min(d << 1, deg)):
            if f[j]:
                res[j] = MOD - f[j]
            else:
                res[j] = 0
        d <<= 1
    return res
def fps_pow(a: list, k: int, deg=-1) -> list:
    n = len(a)
    if deg == -1:
        deg = n
    if k == 0:
        if not deg:
            return []
        ret = [0] * deg
        ret[0] = 1
        return ret
    for i, x in enumerate(a):
        if x:
            rev = pow(x, MOD - 2, MOD)
            ret = fps_mul_scalar(
                fps_exp(
                    fps_mul_scalar(fps_log(fps_mul_scalar(a, rev)[i:], deg), k), deg
                ),
                pow(x, k, MOD),
            )
            ret[:0] = [0] * (i * k)
            if len(ret) < deg:
                ret[len(ret) :] = [0] * (deg - len(ret))
                return ret
            return ret[:deg]
        if (i + 1) * k >= deg:
            break
    return [0] * deg
def fps_exp(a: list, deg=-1) -> list:
    # assert(not self or self[0] == 0)
    if deg == -1:
        deg = len(a)
    inv = [0, 1]
    def inplace_integral(F: list) -> list:
        n = len(F)
        while len(inv) <= n:
            j, k = divmod(MOD, len(inv))
            inv.append((-inv[k] * j) % MOD)
        return [0] + [x * inv[i + 1] % MOD for i, x in enumerate(F)]
    def inplace_diff(F: list) -> list:
        return [x * i % MOD for i, x in enumerate(F) if i]
    b = [1, (a[1] if 1 < len(a) else 0)]
    c = [1]
    z1 = []
    z2 = [1, 1]
    m = 2
    while m < deg:
        y = b + [0] * m
        ntt(y)
        z1 = z2
        z = [y[i] * p % MOD for i, p in enumerate(z1)]
        intt(z)
        z[: m >> 1] = [0] * (m >> 1)
        ntt(z)
        for i, p in enumerate(z1):
            z[i] = z[i] * (-p) % MOD
        intt(z)
        c[m >> 1 :] = z[m >> 1 :]
        z2 = c + [0] * m
        ntt(z2)
        tmp = min(len(a), m)
        x = a[:tmp] + [0] * (m - tmp)
        x = inplace_diff(x)
        x.append(0)
        ntt(x)
        for i, p in enumerate(x):
            x[i] = y[i] * p % MOD
        intt(x)
        for i, p in enumerate(b):
            if not i:
                continue
            x[i - 1] -= p * i % MOD
        x += [0] * m
        for i in range(m - 1):
            x[m + i], x[i] = x[i], 0
        ntt(x)
        for i, p in enumerate(z2):
            x[i] = x[i] * p % MOD
        intt(x)
        x.pop()
        x = inplace_integral(x)
        x[:m] = [0] * m
        for i in range(m, min(len(a), m << 1)):
            x[i] += a[i]
        ntt(x)
        for i, p in enumerate(y):
            x[i] = x[i] * p % MOD
        intt(x)
        b[m:] = x[m:]
        m <<= 1
    return b[:deg]
def fps_log(a: list, deg=-1) -> list:
    # assert(a[0] == 1)
    if deg == -1:
        deg = len(a)
    return fps_integral(multiply(fps_diff(a), fps_inv(a, deg))[: deg - 1])
def fps_integral(a: list) -> list:
    n = len(a)
    res = [0] * (n + 1)
    if n:
        res[1] = 1
    for i in range(2, n + 1):
        j, k = divmod(MOD, i)
        res[i] = (-res[k] * j) % MOD
    for i, x in enumerate(a):
        res[i + 1] = res[i + 1] * x % MOD
    return res
def fps_diff(a: list) -> list:
    return [i * x % MOD for i, x in enumerate(a) if i]
# https://judge.yosupo.jp/problem/inv_of_formal_power_series
N, K = map(int, input().split())
K1, K2 = (K + 1) // 2, K // 2
A = list(map(int, input().split()))
# wtnl(fps_inv(A))
inv_mod = [pow(x, MOD - 2, MOD) for x in range(N + 1)]
B1 = [1 for i in range(N)]
B2 = [1 for i in range(N)]
for i in range(1, N):
    B1[i] = -B1[i - 1] * inv_mod[i] * (K1 - i + 1) % MOD
    B2[i] = B2[i - 1] * inv_mod[i] * (K2 - i + 1) % MOD
B = multiply(B1, B2)
if K & 1:
    A = [-A[i] if i & 1 else A[i] for i in range(N)]
C = multiply(A, fps_inv(B))
print(*[C[i] % MOD for i in range(N)])
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