結果

問題 No.3445 Sum of (Tree Distances)^K 2
コンテスト
ユーザー 👑 potato167
提出日時 2026-02-05 16:41:57
言語 PyPy3
(7.3.17)
結果
AC  
実行時間 2,870 ms / 4,000 ms
コード長 7,162 bytes
記録
記録タグの例:
初AC ショートコード 純ショートコード 純主流ショートコード 最速実行時間
コンパイル時間 315 ms
コンパイル使用メモリ 82,552 KB
実行使用メモリ 202,216 KB
最終ジャッジ日時 2026-02-06 20:58:14
合計ジャッジ時間 48,096 ms
ジャッジサーバーID
（参考情報） 		judge3 / 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 * 47
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 #
raw source code 

# https://judge.yosupo.jp/submission/222202

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)

L = (1 << 18)
fact = [1] * (L + 1)
inv_fact = [1] * (L + 1)
for i in range(L):
    fact[i + 1] = fact[i] * (i + 1) % mod
inv_fact[L] = pow(fact[L], mod - 2, mod)
for i in range(L, 1, -1):
    inv_fact[i - 1] = inv_fact[i] * i % mod

MAX_S = 1 << 18
ctz1 = [0] * MAX_S
for s in range(MAX_S):
    t = (s + 1) & (-(s + 1))
    ctz1[s] = t.bit_length()

def fft(a):
    n = len(a)
    h = (n - 1).bit_length()
    le = 0
    while le < h:
        if h == le + 1:
            p = 1
            rot = 1
            for s in range(1 << le):
                offset = s << (h - le)
                for i in range(p):
                    l = a[i + offset]
                    r = a[i + offset + p] * rot % mod
                    a[i + offset] = (l + r if l + r < mod else l + r - mod)
                    a[i + offset + p] = (l - r) % mod
                rot = rot * rate2[ctz1[s]] % mod
            le += 1
        else:
            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[ctz1[s]] % mod
            le += 2

def fft_inv(a):
    n = len(a)
    h = (n - 1).bit_length()
    le = h
    while le:
        if le == 1:
            p = 1 << (h - le)
            irot = 1
            for 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 if l + r < mod else l + r - mod)
                    a[i + offset + p] = (l - r) * irot % mod
                irot *= irate2[ctz1[s]]
                irot %= mod
            le -= 1
        else:
            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 *= irate3[ctz1[s]]
                irot %= mod
            le -= 2

def ntt(a):
    if len(a) <= 1:
        return
    fft(a)

def ntt_inv(a):
    if len(a) <= 1:
        return
    fft_inv(a)
    iv = pow(len(a),mod-2,mod)
    for i in range(len(a)):
        a[i] = a[i] * iv % mod

def convolute(a,b):
    aa = a[:]
    bb = b[:]
    n = len(aa)
    m = len(bb)
    if min(n,m) <= 120:
        return convolute_naive(a,b)
    z = 1 << (n + m - 2).bit_length()
    aa += [0] * (z - n)
    bb += [0] * (z - m)
    fft(aa)
    fft(bb)
    for i in range(z):
        aa[i] = aa[i] * bb[i] % mod
    fft_inv(aa)
    aa = aa[:n + m - 1]
    iz = pow(z, mod - 2, mod)
    for i in range(n+m-1):
        aa[i] = (aa[i] * iz) % mod
    return aa

def convolute_naive(a,b):
    res = [0] * (len(a) + len(b) - 1)
    for i in range(len(a)):
        for j in range(len(b)):
            res[i+j] = (res[i+j] + a[i] * b[j] % mod) % mod
    return res

def convolute_slice(a : list[int], b : list[int], l : int, r : int) -> list[int]:
    if r < 30:
        res = [0] * (r - l)
        for i in range(len(a)):
            for j in range(max(0, l - i), min(len(b), r - i)):
                res[i + j - l] = (res[i + j - l] + a[i] * b[j] % mod) % mod
        return res
    else:
        n = len(a) + len(b) - 2
        m = max(len(a), len(b))
        sz = 1
        while sz < m or r > sz or n >= l + sz:
            sz *= 2
        na = a[:]
        nb = b[:]
        na += [0] * (sz - len(na))
        nb += [0] * (sz - len(nb))
        fft(na)
        fft(nb)
        iz = pow(sz, mod - 2, mod)
        for i in range(sz):
            na[i] = na[i] * nb[i] % mod
            na[i] = na[i] * iz % mod
        fft_inv(na)
        return na[l : r]

N, K = map(int, input().split())


g = [1] * N
for i in range(N):
    g[i] = pow(N - i - 1, K, mod)


def f(l : int, r : int, v : list[int], ans : list[int]) -> tuple[list[int], list[int]]:
    if l + 1 == r:
        ans[l] = v[-1]
        return [l + 1], [l + 1, 2]
    m = (l + r) // 2
    nv = [0] * (m - l)
    for i in range(m - l):
        nv[i] = v[i + r - m]
    LA, LB = f(l, m, nv, ans)
    nv = [0] * (r - m)
    nv1 = convolute_slice(v, LB, m - l, r - l)
    ng = [0] * (r - l)
    for i in range(r - l):
        ng[i] = g[i + N - r + l]
    nv2 = convolute_slice(ng, LA, m - l, r - l)
    for i in range(r - m):
        nv[i] = (nv1[i] + nv2[i] * fact[l]) % mod
    RA, RB = f(m, r, nv, ans)
    if r == N:
        return [], []
    nA = convolute(LA, RB)
    tmp = fact[m] * inv_fact[l] % mod
    for i, a in enumerate(RA):
        nA[i] = (nA[i] + a * tmp) % mod
    return nA, convolute(LB, RB)

ans = [0] * N
f(0, N, g, ans)

res = [0] * N
for i in range(1, N):
    res[i] = (ans[i] - ans[i - 1] * i) % mod
    res[i] = res[i] * fact[N - 1] % mod
    res[i] = res[i] * inv_fact[i] % mod
# print(sum(res))
for i in range(N):
    print(res[i] * inv_fact[2] % mod)
0