#863185 (PyPy3) No.1321 塗るめた

提出ソース

結果

問題	No.1321 塗るめた
ユーザー	vwxyz
提出日時	2023-04-27 01:53:22
言語	PyPy3 (7.3.15)
結果	TLE
実行時間	-
コード長	16,124 bytes
コンパイル時間	256 ms
コンパイル使用メモリ	82,428 KB
実行使用メモリ	282,308 KB
最終ジャッジ日時	2024-11-16 09:40:31
合計ジャッジ時間	49,481 ms
ジャッジサーバーID （参考情報）	judge5 / judge2

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	45 ms 57,856 KB
testcase_01	AC	234 ms 81,244 KB
testcase_02	AC	47 ms 58,240 KB
testcase_03	AC	46 ms 57,984 KB
testcase_04	AC	49 ms 58,112 KB
testcase_05	AC	43 ms 57,600 KB
testcase_06	AC	43 ms 57,984 KB
testcase_07	AC	49 ms 63,744 KB
testcase_08	AC	57 ms 67,584 KB
testcase_09	AC	74 ms 74,368 KB
testcase_10	AC	46 ms 57,344 KB
testcase_11	AC	108 ms 77,440 KB
testcase_12	AC	1,201 ms 241,928 KB
testcase_13	AC	404 ms 108,384 KB
testcase_14	AC	653 ms 148,848 KB
testcase_15	AC	1,163 ms 242,620 KB
testcase_16	AC	1,209 ms 244,500 KB
testcase_17	AC	207 ms 79,104 KB
testcase_18	TLE	-
testcase_19	AC	679 ms 150,148 KB
testcase_20	AC	1,198 ms 238,292 KB
testcase_21	AC	1,124 ms 236,500 KB
testcase_22	TLE	-
testcase_23	TLE	-
testcase_24	TLE	-
testcase_25	TLE	-
testcase_26	TLE	-
testcase_27	TLE	-
testcase_28	TLE	-
testcase_29	TLE	-
testcase_30	TLE	-
testcase_31	AC	1,229 ms 243,876 KB
testcase_32	AC	1,231 ms 239,468 KB
testcase_33	AC	1,213 ms 237,672 KB
testcase_34	AC	1,255 ms 243,768 KB
testcase_35	AC	1,239 ms 239,584 KB
testcase_36	AC	69 ms 73,856 KB
testcase_37	AC	1,218 ms 244,276 KB
testcase_38	AC	1,266 ms 244,544 KB
testcase_39	AC	1,274 ms 244,368 KB
testcase_40	AC	1,115 ms 236,064 KB
testcase_41	AC	1,174 ms 244,460 KB
testcase_42	AC	46 ms 57,680 KB
testcase_43	AC	1,189 ms 239,984 KB
testcase_44	AC	1,191 ms 238,116 KB
testcase_45	AC	1,187 ms 243,644 KB
testcase_46	AC	410 ms 106,480 KB

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

raw source code

from collections import deque
import math
import sys
readline=sys.stdin.readline

mod = 998244353

class FFT:
    def __init__(self, mod=998244353):
        FFT.mod = mod
        self.make_info(mod)

    def make_info(self, mod):
        g = self.primitive_root_constexpr()
        m = mod - 1
        rank2 = (m & -m).bit_length() - 1
        root = [0] * (rank2 + 1)
        iroot = [0] * (rank2 + 1)
        rate2 = [0] * (rank2 + 1)
        irate2 = [0] * (rank2 + 1)
        rate3 = [0] * (rank2)
        irate3 = [0] * (rank2)

        root[rank2] = pow(g, (mod - 1) >> rank2, mod)
        iroot[rank2] = pow(root[rank2], mod - 2, mod)
        for i in range(rank2 - 1, -1, -1):
            root[i] = root[i + 1] * root[i + 1] % mod
            iroot[i] = iroot[i + 1] * iroot[i + 1] % mod

        prod = 1
        iprod = 1
        for i in range(1, rank2):
            rate2[i] = root[i + 1] * prod % mod
            irate2[i] = iroot[i + 1] * iprod % mod
            prod = prod * iroot[i + 1] % mod
            iprod = iprod * root[i + 1] % mod

        prod = 1
        iprod = 1
        for i in range(1, rank2 - 1):
            rate3[i] = root[i + 2] * prod % mod
            irate3[i] = iroot[i + 2] * iprod % mod
            prod = prod * iroot[i + 2] % mod
            iprod = iprod * root[i + 2] % mod

        self.IMAG = rate2[1]
        self.IIMAG = irate2[1]
        self.rate2 = rate2
        self.irate2 = irate2
        self.rate3 = rate3
        self.irate3 = irate3

    def primitive_root_constexpr(self):
        if FFT.mod == 998244353:
            return 3
        elif FFT.mod == 200003:
            return 2
        elif FFT.mod == 167772161:
            return 3
        elif FFT.mod == 469762049:
            return 3
        elif FFT.mod == 754974721:
            return 11
        divs = [0] * 20
        divs[0] = 2
        cnt = 1
        x = (FFT.mod - 1) // 2
        while x % 2 == 0:
            x //= 2
        i = 3
        while i * i <= x:
            if x % i == 0:
                divs[cnt] = i
                cnt += 1
                while x % i == 0:
                    x //= i
            i += 2
        if x > 1:
            divs[cnt] = x
            cnt += 1
        g = 2
        while 1:
            ok = True
            for i in range(cnt):
                if pow(g, (FFT.mod - 1) // divs[i], FFT.mod) == 1:
                    ok = False
                    break
            if ok:
                return g
            g += 1

    def butterfly(self, A):
        n = len(A)
        h = (n - 1).bit_length()
        le = 0
        while le < h:
            if h - le == 1:
                p = 1 << (h - le - 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) % FFT.mod
                        A[i + offset + p] = (l - r) % FFT.mod
                    rot *= self.rate2[(~s & -~s).bit_length()]
                    rot %= FFT.mod
                le += 1
            else:
                p = 1 << (h - le - 2)
                rot = 1
                for s in range(1 << le):
                    rot2 = rot * rot % FFT.mod
                    rot3 = rot2 * rot % FFT.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) % FFT.mod * self.IMAG
                        A[i + offset] = (a0 + a2 + a1 + a3) % FFT.mod
                        A[i + offset + p] = (a0 + a2 - a1 - a3) % FFT.mod
                        A[i + offset + p * 2] = (a0 - a2 + a1na3imag) % FFT.mod
                        A[i + offset + p * 3] = (a0 - a2 - a1na3imag) % FFT.mod
                    rot *= self.rate3[(~s & -~s).bit_length()]
                    rot %= FFT.mod
                le += 2

    def butterfly_inv(self, 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) % FFT.mod
                        A[i + offset + p] = (l - r) * irot % FFT.mod
                    irot *= self.irate2[(~s & -~s).bit_length()]
                    irot %= FFT.mod
                le -= 1
            else:
                p = 1 << (h - le)
                irot = 1
                for s in range(1 << (le - 2)):
                    irot2 = irot * irot % FFT.mod
                    irot3 = irot2 * irot % FFT.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) * self.IIMAG % FFT.mod
                        A[i + offset] = (a0 + a1 + a2 + a3) % FFT.mod
                        A[i + offset + p] = (a0 - a1 + a2na3iimag) * irot % FFT.mod
                        A[i + offset + p * 2] = (a0 + a1 - a2 - a3) * irot2 % FFT.mod
                        A[i + offset + p * 3] = (a0 - a1 - a2na3iimag) * irot3 % FFT.mod
                    irot *= self.irate3[(~s & -~s).bit_length()]
                    irot %= FFT.mod
                le -= 2

    def convolve(self, A, B):
        n = len(A)
        m = len(B)
        if min(n, m) <= 60:
            C = [0] * (n + m - 1)
            for i in range(n):
                if i % 8 == 0:                
                    for j in range(m):
                        C[i + j] += A[i] * B[j]
                        C[i + j] %= FFT.mod
                else:
                    for j in range(m):
                        C[i + j] += A[i] * B[j]
            return [c % FFT.mod for c in C]
        A = A[:]
        B = B[:]
        z = 1 << (n + m - 2).bit_length()
        A += [0] * (z - n)
        B += [0] * (z - m)
        self.butterfly(A)
        self.butterfly(B)
        for i in range(z):
            A[i] *= B[i]
            A[i] %= FFT.mod
        self.butterfly_inv(A)
        A = A[:n + m - 1]
        iz = pow(z, FFT.mod - 2, FFT.mod)
        return [a * iz % FFT.mod for a in A]

class FPS:
    fact = [1]
    invfact = [1]
    mod = None
    def __init__(self, data, mod=998244353):
        if FPS.mod is None:
            FPS.mod = mod
            FPS.fft = FFT(mod)
        if type(data) == int:
            self.f = [data]
        else:
            self.f = data[:]

    def __len__(self):
        return len(self.f)

    def __getitem__(self, i):
        return self.f[i]
    
    def __add__(self, other):
        if len(self) < len(other):
            other, self = self, other
        for i in range(len(other)):
            self.f[i] += other[i]
            if self.f[i] >= FPS.mod:
                self.f[i] -= FPS.mod
        return self
    
    def __iadd__(self, other):
        return self.__add__(other)

    def __sub__(self, other):
        self.f += [0] * (len(other) - len(self))
        for i in range(len(other)):
            self.f[i] -= other[i]
            if self.f[i] < 0:
                self.f[i] += FPS.mod
        return self

    def __isub__(self, other):
        return self.__sub__(other)

    def __mul__(self, other):
        if type(other) == int:
            f = [other * x % FPS.mod for x in self.f]
            return FPS(f)
        f = FPS.fft.convolve(self.f[:], other.f[:])
        return FPS(f)

    def __imul__(self, other):
        if type(other) == int:
            self.f = [other * x % FPS.mod for x in self.f]
            return self
        self.f = FPS.fft.convolve(self.f, other.f[:])
        return self

    def inv(self, deg=None):
        if deg is None:
            deg = len(self)
        g = FPS(pow(self[0], FPS.mod - 2, FPS.mod))
        l = 1
        while l < deg:
            tmp = g * 2
            l *= 2
            tmp2 = FPS(self.f[:l]) * (g * g)
            g = tmp - tmp2
            del g.f[l:]
        del g.f[deg:]
        return g

    def differential(self):
        return FPS([x * i % FPS.mod for i, x in enumerate(self.f[1:], 1)])
    
    def extend_fact(self, l):
        l1 = len(FPS.fact)
        l += 1
        if l1 <= l:
            FPS.fact += [0] * (l - l1)
            FPS.invfact += [0] * (l - l1)
            for i in range(l1, l):
                FPS.fact[i] = FPS.fact[i - 1] * i % FPS.mod
            FPS.invfact[l - 1] = pow(FPS.fact[l - 1], FPS.mod - 2, FPS.mod)
            for i in range(l - 1, l1, -1):
                FPS.invfact[i - 1] = FPS.invfact[i] * i % FPS.mod

    def integral(self):        
        self.extend_fact(len(self))
        return FPS([0] + [x * (FPS.fact[i] * FPS.invfact[i + 1] % FPS.mod) % FPS.mod for i, x in enumerate(self.f)])

    def log(self, deg=None):
        if deg is None:
            deg = len(self)
        tmp = self.differential() * self.inv(deg=deg)
        del tmp.f[deg:]
        tmp = tmp.integral()
        del tmp.f[deg:]
        return tmp

    def exp(self, deg=None):
        if deg is None:
            deg = len(self)
        g = FPS(1)
        l = 1
        while l < deg * 2:
            l *= 2
            log = FPS(1) - g.log(deg=l) + FPS(self.f[:l])
            del log.f[l:]
            g *= log
            del g.f[l:]
        del g.f[deg:]
        return g

    def __pow__(self, k, deg=None):
        if k == 0:
            if deg is None:
                ret = [0] * len(self)
            else:
                ret = [0] * deg
            ret[0] = 1
            return FPS(ret)
        if deg is None:
            deg = len(self)
        i = 0
        p = None
        for i in range(deg):
            if self[i] != 0:
                a = self[i]
                p = i
                break
        if p is None:
            if deg is not None:
                return FPS([0] * deg)
            else:
                return FPS(0)
        elif deg is not None and p * k >= deg:
            return FPS([0] * deg)
        inv = pow(a, FPS.mod - 2, FPS.mod)
        tmp = FPS([x * inv % FPS.mod for x in self.f[p:]])
        tmp = tmp.log(deg=deg)
        if deg is not None:
            del tmp.f[deg:]
        tmp *= k        
        tmp = tmp.exp(deg=deg)
        tmp = [0] * (p * k) + tmp.f[:deg - p * k]
        times = pow(a, k, FPS.mod)
        return FPS([x * times % FPS.mod for x in tmp])
    
    def __ipow__(self, k):
        return self.__pow__(k)

    def cipolla(self, a):
        if FPS.mod == 2:
            return a
        elif a == 0:
            return 0
        elif pow(a, (FPS.mod - 1) // 2, FPS.mod) != 1:
            return -1
        b = 0
        while pow((b * b + FPS.mod - a) % FPS.mod, (FPS.mod - 1) // 2, FPS.mod) == 1:
            b += 1
        
        base = b * b + FPS.mod - a
        
        def multi(a0, b0, a1, b1):
            return (a0 * a1 + (b0 * b1 % FPS.mod) * base) % FPS.mod, (a0 * b1 + b0 * a1) % FPS.mod

        def pow_(a, b, n):
            if n == 0:
                return 1, 0
            a_, b_ = pow_(*multi(a, b, a, b), n // 2)
            if n % 2 == 1:
                a_, b_ = multi(a_, b_, a, b)
            return a_, b_

        return pow_(b, 1, (FPS.mod + 1) // 2)[0]

    def sqrt(self, deg=None):
        if deg is None:
            deg = len(self)
        if len(self) == 0:
            return FPS([0] * deg)
        if self[0] == 0:
            for i in range(1, len(self)):
                if self[i] != 0:
                    if i & 1:
                        return FPS([])
                    if deg <= i // 2:
                        break
                    ret = FPS(self.f[i:]).sqrt(deg - i // 2)
                    if len(ret) == 0:
                        return FPS([])
                    ret.f = [0] * (i // 2) + ret.f
                    if len(ret) < deg:
                        ret.f += [0] * (deg - len(ret))
                    return ret
            return FPS([0] * deg)
        
        sq = self.cipolla(self[0])
        if sq == -1:
            return FPS([])
        inv2 = (FPS.mod + 1) // 2
        g = FPS([sq])
        l = 1
        while l < deg:
            l *= 2
            tmp = FPS(self.f[:l]) * g.inv(deg=l)
            g += tmp
            g *= inv2

        del g.f[deg:]
        return g

    def taylorshift(self, a):
        deg = len(self)
        f = self.f[:]
        self.extend_fact(deg)
        for i in range(deg):
            f[i] *= FPS.fact[i]
            f[i] %= FPS.mod
        f = f[::-1]
        g = [0] * deg
        g[0] = 1
        for i in range(1, deg):
            g[i] = (g[i - 1] * a % FPS.mod) * (FPS.fact[i - 1] * FPS.invfact[i] % FPS.mod) % FPS.mod
        f = FPS.fft.convolve(f, g)
        del f[deg:]
        f = f[::-1]
        for i in range(deg):
            f[i] *= FPS.invfact[i]
            f[i] %= FPS.mod
        return FPS(f)

def Extended_Euclid(n,m):
    stack=[]
    while m:
        stack.append((n,m))
        n,m=m,n%m
    if n>=0:
        x,y=1,0
    else:
        x,y=-1,0
    for i in range(len(stack)-1,-1,-1):
        n,m=stack[i]
        x,y=y,x-(n//m)*y
    return x,y

class MOD:
    def __init__(self,p,e=None):
        self.p=p
        self.e=e
        if self.e==None:
            self.mod=self.p
        else:
            self.mod=self.p**self.e

    def Pow(self,a,n):
        a%=self.mod
        if n>=0:
            return pow(a,n,self.mod)
        else:
            assert math.gcd(a,self.mod)==1
            x=Extended_Euclid(a,self.mod)[0]
            return pow(x,-n,self.mod)

    def Build_Fact(self,N):
        assert N>=0
        self.factorial=[1]
        if self.e==None:
            for i in range(1,N+1):
                self.factorial.append(self.factorial[-1]*i%self.mod)
        else:
            self.cnt=[0]*(N+1)
            for i in range(1,N+1):
                self.cnt[i]=self.cnt[i-1]
                ii=i
                while ii%self.p==0:
                    ii//=self.p
                    self.cnt[i]+=1
                self.factorial.append(self.factorial[-1]*ii%self.mod)
        self.factorial_inve=[None]*(N+1)
        self.factorial_inve[-1]=self.Pow(self.factorial[-1],-1)
        for i in range(N-1,-1,-1):
            ii=i+1
            while ii%self.p==0:
                ii//=self.p
            self.factorial_inve[i]=(self.factorial_inve[i+1]*ii)%self.mod

    def Fact(self,N):
        if N<0:
            return 0
        retu=self.factorial[N]
        if self.e!=None and self.cnt[N]:
            retu*=pow(self.p,self.cnt[N],self.mod)%self.mod
            retu%=self.mod
        return retu

    def Fact_Inve(self,N):
        if self.e!=None and self.cnt[N]:
            return None
        return self.factorial_inve[N]

    def Comb(self,N,K,divisible_count=False):
        if K<0 or K>N:
            return 0
        retu=self.factorial[N]*self.factorial_inve[K]%self.mod*self.factorial_inve[N-K]%self.mod
        if self.e!=None:
            cnt=self.cnt[N]-self.cnt[N-K]-self.cnt[K]
            if divisible_count:
                return retu,cnt
            else:
                retu*=pow(self.p,cnt,self.mod)
                retu%=self.mod
        return retu

N,M,K=map(int,readline().split())
mod=998244353
MD=MOD(mod)
MD.Build_Fact(N)
poly=[None]*(N-K+1)
for i in range(N-K+1):
    poly[i]=MD.Fact_Inve(i+1)
P=FPS(poly)
P=P.log(deg=N-K+1)
for i in range(N-K+1):
    P.f[i]*=K
    P.f[i]%=mod
P=P.exp(deg=N-K+1)
ans=0
for n in range(K,N+1):
    ans+=P[n-K]*MD.Pow(M,N-n)%mod*MD.Fact_Inve(N-n)%mod
ans*=MD.Comb(M,K)*MD.Fact(N)%mod
ans%=mod
print(ans)

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結果

テストケース

ソースコード