結果

問題 No.3450 Permutation of Even Scores
コンテスト
ユーザー 👑 potato167
提出日時 2026-02-09 15:10:52
言語 PyPy3
(7.3.17)
結果
AC  
実行時間 1,407 ms / 2,000 ms
コード長 5,609 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 196 ms
コンパイル使用メモリ 82,436 KB
実行使用メモリ 155,172 KB
最終ジャッジ日時 2026-02-20 20:54:23
合計ジャッジ時間 51,516 ms
ジャッジサーバーID
（参考情報） 		judge2 / judge3
このコードへのチャレンジ
（要ログイン）
ファイルパターン 結果
sample AC * 4
other AC * 46
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 

# FFT はパクリ
# 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)

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
                    a[i + offset] = (l + r) % mod
                    a[i + offset + p] = (l - r) % mod
                rot *= rate2[(~s & -~s).bit_length()]
                rot %= 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 *= rate3[(~s & -~s).bit_length()]
                rot %= 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) % mod
                    a[i + offset + p] = (l - r) * irot % mod
                irot *= irate2[(~s & -~s).bit_length()]
                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[(~s & -~s).bit_length()]
                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) <= 60:
        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

N, M = map(int, input().split())
A = [0] * N
for a in map(int, input().split()):
    A[a - 1] = 1
fact = [1] * (N + 1)
for i in range(N):
    fact[i + 1] = fact[i] * (i + 1) % mod

dp = [0] * N

ans = fact[N] * 2 % mod

def f(l : int, r : int):
    if l + 1 == r:
        if A[l]:
            dp[l] = (dp[l] + fact[l + 1]) % mod
            dp[l] = (dp[l] * -2) % mod
        else:
            dp[l] = 0
        return
    m = (l + r) // 2
    f(l, m)
    X = dp[l : m]
    Y = fact[1 : r - l + 1]
    Z = convolute(X, Y)
    for i in range(m, r):
        dp[i] = (dp[i] + Z[i - l]) % mod
    f(m, r)
f(0, N)
for i in range(N):
    ans = (ans + dp[i] * fact[N - i]) % mod
if ans & 1:
    ans += mod
print(ans // 2)
0