結果

問題 No.1392 Don't be together
コンテスト
ユーザー chineristAC
提出日時 2020-09-09 02:25:44
言語 PyPy3
(7.3.15)
結果
AC  
実行時間 447 ms / 2,000 ms
コード長 4,474 bytes
コンパイル時間 234 ms
コンパイル使用メモリ 81,920 KB
実行使用メモリ 112,236 KB
最終ジャッジ日時 2024-11-30 19:01:20
合計ジャッジ時間 8,438 ms
ジャッジサーバーID
（参考情報） 		judge5 / judge3
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 * 27
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 # 

mod = 998244353
omega = pow(3,119,mod)
rev_omega = pow(omega,mod-2,mod)

def cmb(n, r, mod):#コンビネーションの高速計算　
    if ( r<0 or r>n ):
        return 0
    r = min(r, n-r)
    return g1[n] * g2[r] * g2[n-r] % mod

N = 2*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]

def inverse(f,limit):
    assert(f[0]!=0)
    l = len(f)
    L = 1<<((l-1).bit_length())
    n = L.bit_length()-1
    f = f[:L]
    f+=[0]*(L-len(f))

    res = [pow(f[0],mod-2,mod)]
    for i in range(1,n+1):
        h = convolve(res,f[:2**i],2**i)
        h = [(-h[i]) % mod for i in range(2**i)]
        h[0] = (h[0]+2) % mod
        res = convolve(res,h,2**i)
    return res[:limit]

def integral(f,limit):
    res = [0]+[(f[i] * inv[i+1]) % mod for i in range(len(f)-1)]
    return res[:limit]

def diff(f,limit):
    res = [(f[i+1] * (i+1)) % mod for i in range(len(f)-1)]+[0]
    return res[:limit]

def log(f,limit):
    res = convolve(diff(f,limit),inverse(f,limit),limit)
    return integral(res,limit)

def exp(f,limit):
    l = len(f)
    L = 1<<((l-1).bit_length())
    n = L.bit_length()-1
    f = f[:L]
    f+=[0]*(L-len(f))

    res = [1]
    for i in range(1,n+1):
        res += [0]*2**(i-1)
        g = log(res,2**i)
        h = [(f[j]-g[j])%mod for j in range(2**i)]
        h[0] = (h[0]+1) % mod
        res =convolve(res,h,2**i)
    return res[:limit]

def poly_pow_exp(f,k,limit):
    l = len(f)
    L = 1<<((l-1).bit_length())
    n = L.bit_length()-1
    f = f[:L]
    f+=[0]*(L-len(f))

    g = log(f,limit)
    g = [(k * g[i]) % mod for i in range(len(g))]
    h = exp(g,limit)
    return h[:limit]

N,M = map(int,input().split())
P = list(map(int,input().split()))

P = [P[i]-1 for i in range(N)]
cycle = []
used = [False]*N
for i in range(N):
    if not used[i]:
        used[i] = True
        c = 1
        pos = i
        while not used[P[pos]]:
            pos = P[pos]
            used[pos] = True
            c += 1
        cycle.append(c)

n = len(cycle)

binom_poly = []
for i in range(n):
    c = [cmb(cycle[i],j,mod) for j in range(1,cycle[i]+1)]
    for j in range(0,cycle[i],2):
        c[j] = (- c[j]) % mod
    c[0] = (c[0] + 1) % mod
    binom_poly.append(c)

while True:
    if len(binom_poly)==1:
        break
    n_binom_poly = []
    while binom_poly:
        f = binom_poly.pop()
        if not binom_poly:
            n_binom_poly.append(f)
            break
        g = binom_poly.pop()
        h = convolve(f,g,len(f)+len(g)-1)
        n_binom_poly.append(h)
    binom_poly = n_binom_poly

poly_f = binom_poly[0]

g = [g2[i+1] for i in range(N+1)]
g = poly_pow_exp(g,M,N+1)

poly_Stirling = [0 for i in range(N+1)]
for i in range(N-M+1):
    poly_Stirling[i+M] = (g[i] * g1[i+M]) % mod
    poly_Stirling[i+M] = (g2[M] * poly_Stirling[i+M]) % mod

ans = 0
for j in range(N-n+1):
    ans += poly_Stirling[n+j] * poly_f[j]
    ans %= mod
print((ans*(-1)**N)%mod)
0