結果

問題 No.1387 Mitarushi's Remodeling
ユーザー chineristAC
提出日時 2021-02-07 22:03:39
言語 PyPy3
(7.3.15)
結果
AC  
実行時間 1,044 ms / 2,000 ms
コード長 2,580 bytes
コンパイル時間 239 ms
コンパイル使用メモリ 82,176 KB
実行使用メモリ 300,748 KB
最終ジャッジ日時 2024-07-04 15:36:01
合計ジャッジ時間 62,273 ms
ジャッジサーバーID
（参考情報） 		judge1 / judge5
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 * 67
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

mod = 998244353
omega = pow(3,119,mod)
rev_omega = pow(omega,mod-2,mod)
N = 5*10**5
g1 = [1]*(N+1) # 元テーブル
g2 = [1]*(N+1) #逆元テーブル
inv = [1]*(N+1) #逆元テーブル計算用テーブル
for i in range( 2, N + 1 ):
    g1[i]=( ( g1[i-1] * i ) % mod )
    inv[i]=( ( -inv[mod % i] * (mod//i) ) % mod )
    g2[i]=( (g2[i-1] * inv[i]) % mod )
inv[0]=0
def _ntt(f,L,reverse=False):
    F=[f[i] for i in range(L)]
    n = L.bit_length() - 1
    base = omega
    if reverse:
        base = rev_omega
    if not n:
        return F
    size = 2**n
    wj = pow(base,2**22,mod)
    res = [0]*2**n
    for i in range(n,0,-1):
        use_omega = pow(base,2**(22+i-n),mod)
        res = [0]*2**n
        size //= 2
        w = 1
        for j in range(0,L//2,size):
            for a in range(size):
                res[a+j] = (F[a+2*j] + w * F[a+size+2*j]) % mod
                t = (w * wj) % mod
                res[L//2+a+j] = (F[a+2*j] + t * F[a+size+2*j]) % mod
            w = (w * use_omega) % mod
        F = res
    return res
def ntt(f,L=0):
    l = len(f)
    if not L:
        L = 1<<((l-1).bit_length())
    while len(f)<L:
        f.append(0)
    f=f[:L]
    F = _ntt(f,L)
    return F
def intt(f,L=0):
    l = len(f)
    if not L:
        L = 1<<((l-1).bit_length())
    while len(f)<L:
        f.append(0)
    f=f[:L]
    F = _ntt(f,L,reverse=True)
    inv = pow(L,mod-2,mod)
    for i in range(L):
        F[i] *= inv
        F[i] %= mod
    return F
def convolve(f,g,limit):
    l = len(f)+len(g)-1
    L = 1<<((l-1).bit_length())
    F = ntt(f,L)
    G = ntt(g,L)
    H = [(F[i] * G[i]) % mod for i in range(L)]
    h = intt(H,L)
    return h[:limit]
inv2 = pow(2,mod-2,mod)
N,K = map(int,input().split())
M = list(map(int,input().split()))
c = 1
for m in M:
    c *= m
    c %= mod
M = [(M[i]+1)*inv2 % mod for i in range(N)]
Mi = [M[N-i-1] for i in range(N)] 
conv = convolve(M,Mi,2*N)[N-1:]
check = [conv[i]*4 % mod for i in range(N)]
imos = [g2[i] for i in range(N)]
for i in range(1,N):
    imos[i] += imos[i-1]
    imos[i] %= mod
prod = [N-1 for i in range(K+1)]
for i in range(2,K+1):
    prod[i] = (prod[i-1] * (N-i)) % mod
prod[0] = 0
imos_prod = [prod[i] for i in range(K+1)]
for i in range(1,K+1):
    imos_prod[i] += imos_prod[i-1]
    imos_prod[i] %= mod
res = imos_prod[K] * conv[N-1] % mod
for x in range(1,N-1):
    L = 1
    R = min(K,N-1-x)
    tmp = g1[N-1-x] * (imos[N-1-x-L] - imos[N-1-x-R] + g2[N-1-x-R])
    tmp2 = (imos_prod[K] - tmp) % mod
    res += tmp2 * conv[x]
    res %= mod
print(res*c % mod)
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