結果

問題 No.2582 Random Average^K
ユーザー Navier_BoltzmannNavier_Boltzmann
提出日時 2023-12-10 13:33:01
言語 PyPy3
(7.3.15)
結果
TLE  
実行時間 -
コード長 5,178 bytes
コンパイル時間 341 ms
コンパイル使用メモリ 81,920 KB
実行使用メモリ 459,472 KB
最終ジャッジ日時 2024-09-27 04:04:00
合計ジャッジ時間 5,376 ms
ジャッジサーバーID
（参考情報） 		judge1 / judge3
このコードへのチャレンジ
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テストケース

テストケース表示
入力 結果 実行時間
実行使用メモリ
testcase_00 AC 41 ms
58,496 KB
testcase_01 AC 39 ms
52,992 KB
testcase_02 AC 37 ms
53,760 KB
testcase_03 AC 37 ms
52,864 KB
testcase_04 AC 36 ms
52,864 KB
testcase_05 AC 38 ms
52,864 KB
testcase_06 AC 65 ms
72,064 KB
testcase_07 AC 50 ms
64,640 KB
testcase_08 AC 64 ms
72,832 KB
testcase_09 AC 1,204 ms
257,328 KB
testcase_10 TLE -
testcase_11 -- -
testcase_12 -- -
testcase_13 -- -
testcase_14 -- -
testcase_15 -- -
testcase_16 -- -
testcase_17 -- -
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ソースコード

diff # 

N,K = map(int,input().split())
mod = 998244353
def convolution(f,g,mod):
    
    def _convolution(f,g,_mod):

        n = len(bin(len(f)+len(g)-1)) - 2
        fft_length = 1<<n

        f = f + [0]*(fft_length - len(f))
        g = g + [0]*(fft_length - len(g))

        if _mod==998244353:
            w = [1, 998244352, 911660635, 372528824, 929031873, 452798380, 922799308, 781712469, 476477967, 166035806, 258648936, 584193783, 63912897, 350007156, 666702199, 968855178, 629671588, 24514907, 996173970, 363395222, 565042129, 733596141, 267099868, 15311432]
            iw = [1, 998244352, 86583718, 509520358, 337190230, 87557064, 609441965, 135236158, 304459705, 685443576, 381598368, 335559352, 129292727, 358024708, 814576206, 708402881, 283043518, 3707709, 121392023, 704923114, 950391366, 428961804, 382752275, 469870224]
        
        if _mod==897581057:
            w = [1, 897581056, 200527991, 850960045, 227655573, 685177417, 661961559, 717889083, 688546301, 64431346, 762907769, 781659575, 604882016, 471181658, 242773703, 313099125, 288794207, 732004569, 437566725, 430897771, 279727937, 91704119, 523358721, 872686320]
            iw =[1, 897581056, 697053066, 442470459, 502631723, 192192108, 366473218, 285218810, 627498913, 632928577, 715124372, 829482092, 895669752, 835819291, 210274124, 7242324, 530138839, 365592405, 712687518, 812501856, 244025573, 353112847, 793229247, 354917575]

        if _mod==880803841:
            w = [1, 880803840, 121444121, 547680885, 836988352, 170630252, 547743738, 390590270, 755881750, 119481987, 622213777, 634844223, 496183605, 872875137, 41469254, 551868471, 219288049, 198000217, 579409128, 733691905, 566136041, 374515633, 402082372, 273508579]
            iw = [1, 880803840, 759359720, 339414624, 282082127, 83908436, 623501316, 879302015, 26105166, 708522529, 769895303, 843755407, 710708181, 623500536, 528308065, 542164623, 817679620, 571049407, 409417309, 504998132, 352282463, 252040680, 400443141, 109748732]


        def fft(a):

            for i in range(fft_length):
                j = 0
                for k in range(n):
                    j |= ((i>>k)&1) << (n - 1 - k)

                if i<j:
                    a[i],a[j] = a[j],a[i]
            
            for nn in range(n):
                b = 1<<nn
                wj = 1
                _wj = iw[nn+1]
                for j in range(b):


                    for k in range(0,fft_length,2*b):

                        s = a[j+k]
                        t = a[j+k+b]*wj%_mod
                        a[j+k] = (s+t)%_mod
                        a[j+k+b] = (s-t)%_mod

                    wj = wj*_wj%_mod            
            return a
        
        def ifft(a):
            for i in range(fft_length):
                j = 0
                for k in range(n):
                    j |= ((i>>k)&1) << (n - 1 - k)

                if i<j:
                    a[i],a[j] = a[j],a[i]
            
            for nn in range(n):
                b = 1<<nn
                wj = 1
                _wj = w[nn+1]
                for j in range(b):

                    for k in range(0,fft_length,2*b):

                        s = a[j+k]
                        t = a[j+k+b]*wj%_mod
                        a[j+k] = (s+t)%_mod
                        a[j+k+b] = (s-t)%_mod

                    wj = wj*_wj%_mod            
            inv = pow(fft_length,_mod-2,_mod)
            return [i*inv%_mod for i in a]
                
        F = fft(f)
        G = fft(g)
        H = [i*j%_mod for i,j in zip(F,G)]
        return [i for i in ifft(H)]
    
    f = [i%mod for i in f]
    g = [i%mod for i in g]
    
        
    x = _convolution(f,g,998244353)
    if mod==998244353:
        return x
    y = _convolution(f,g,897581057)
    z = _convolution(f,g,880803841)

    m1 = 998244353
    m2 = 897581057
    m3 = 880803841

    m1_inv_m2 = pow(m1,m2-2,m2)
    m12_inv_m3 = pow(m1*m2,m3-2,m3)
    m12_mod = m1*m2%mod

    res = [0]*len(x)

    for i in range(len(x)):

        v1 = (y[i]-x[i])*m1_inv_m2%m2
        v2 = (z[i]-(x[i]+m1*v1)%m3)*m12_inv_m3%m3
        c3 = (x[i]+ m1*v1 + m12_mod*v2)%mod
        res[i] = c3
    
    return res

class combination():

    def __init__(self,N,p):
        
        
        self.fact = [1, 1]  # fact[n] = (n! mod p)
        self.factinv = [1, 1]  # factinv[n] = ((n!)^(-1) mod p)
        self.inv = [0, 1]  # factinv 計算用
        self.p = p
        
        for i in range(2, N + 1):
            self.fact.append((self.fact[-1] * i) % p)
            self.inv.append((-self.inv[p % i] * (p // i)) % p)
            self.factinv.append((self.factinv[-1] * self.inv[-1]) % p)
        

    def cmb(self,n, r):
        if (r < 0) or (n < r):
            return 0
        r = min(r, n - r)
        return self.fact[n] * self.factinv[r] * self.factinv[n-r] % self.p
    
C = combination(K+1+N,mod)

ans = 0
for i in range(N):

    if i%2==0:

        ans += C.cmb(N,i)*pow(N-i,N+K,mod)
        ans %= mod
    else:
        ans -= C.cmb(N,i)*pow(N-i,N+K,mod)
        ans %= mod

inv = pow(C.fact[N+K]*C.factinv[K],mod-2,mod)
ans = (ans*inv)%mod
inv = pow(pow(N,K,mod),mod-2,mod)
print(ans*inv%mod)
0