#924351 (PyPy3) No.2670 Sum of Products of Interval Lengths

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問題	No.2670 Sum of Products of Interval Lengths
ユーザー	suisen
提出日時	2023-10-30 01:16:24
言語	PyPy3 (7.3.15)
結果	AC
実行時間	755 ms / 2,000 ms
コード長	6,285 bytes
コンパイル時間	511 ms
コンパイル使用メモリ	82,468 KB
実行使用メモリ	139,628 KB
最終ジャッジ日時	2024-09-28 17:43:13
合計ジャッジ時間	10,602 ms
ジャッジサーバーID （参考情報）	judge1 / judge2
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ファイルパターン	結果
other	AC * 17
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from typing import List
def bsf(x):
    res = 0
    while not (x & 1):
        res += 1
        x >>= 1
    return res
P = 998244353
G = 3
rank2 = bsf(P - 1)
class NTT:
    class __RootInitializer:
        @staticmethod
        def root():
            return [pow(G, (P - 1) >> i, P) for i in range(0, rank2 + 1)]
        @staticmethod
        def iroot():
            return [pow(pow(G, P - 2, P), (P - 1) >> i, P) for i in range(0, rank2 + 1)]
    root = __RootInitializer.root()
    iroot = __RootInitializer.iroot()
    class __RateInitializer:
        @staticmethod
        def rates(root: List[int], iroot: List[int]):
            rate2 = [0] * max(0, rank2 - 1)
            irate2 = [0] * max(0, rank2 - 1)
            prod = iprod = 1
            for i in range(rank2 - 1):
                rate2[i] = root[i + 2] * prod % P
                irate2[i] = iroot[i + 2] * iprod % P
                prod = prod * iroot[i + 2] % P
                iprod = iprod * root[i + 2] % P
            
            rate3 = [0] * max(0, rank2 - 2)
            irate3 = [0] * max(0, rank2 - 2)
            prod = iprod = 1
            for i in range(rank2 - 2):
                rate3[i] = root[i + 3] * prod % P
                irate3[i] = iroot[i + 3] * iprod % P
                prod = prod * iroot[i + 3] % P
                iprod = iprod * root[i + 3] % P
            return rate2, irate2, rate3, irate3
    
    rate2, irate2, rate3, irate3 = __RateInitializer.rates(__RootInitializer.root(), __RootInitializer.iroot())
    @staticmethod
    def butterfly(a: List[int]) -> None:
        n = len(a)
        h = bsf(n)
        l = 0
        while l < h:
            if h - l == 1:
                p = 1 << (h - l - 1)
                rot = 1
                for s in range(1 << l):
                    offset = s << (h - l)
                    for i in range(p):
                        u = a[i + offset]
                        v = a[i + offset + p] * rot
                        a[i + offset] = (u + v) % P
                        a[i + offset + p] = (u - v) % P
                    if s + 1 != 1 << l:
                        rot = rot * NTT.rate2[bsf(~s)] % P
                l += 1
            else:
                p = 1 << (h - l - 2)
                rot, imag = 1, NTT.root[2]
                for s in range(1 << l):
                    rot2 = rot * rot % P
                    rot3 = rot2 * rot % P
                    offset = s << (h - l)
                    for i in range(p):
                        a0 = a[i + offset]
                        a1 = a[i + offset + p] * rot
                        a2 = a[i + offset + 2 * p] * rot2
                        a3 = a[i + offset + 3 * p] * rot3
                        a1na3imag = (a1 - a3) % P * imag
                        a[i + offset] = (a0 + a2 + a1 + a3) % P
                        a[i + offset + 1 * p] = (a0 + a2 - a1 - a3) % P
                        a[i + offset + 2 * p] = (a0 - a2 + a1na3imag) % P
                        a[i + offset + 3 * p] = (a0 - a2 - a1na3imag) % P
                    if s + 1 != (1 << l):
                        rot = rot * NTT.rate3[bsf(~s)] % P
                l += 2
    @staticmethod
    def butterfly_inv(a : List[int]) -> None:
        n = len(a)
        h = bsf(n)
        l = h
        while l:
            if l == 1:
                p = 1 << (h - l)
                irot = 1
                for s in range(1 << (l - 1)):
                    offset = s << (h - l + 1)
                    for i in range(p):
                        u = a[i + offset]
                        v = a[i + offset + p]
                        a[i + offset] = (u + v) % P
                        a[i + offset + p] = ((u - v) * irot) % P
                    if s + 1 != 1 << (l - 1):
                        irot = irot * NTT.irate2[bsf(~s)] % P
                l -= 1
            else:
                p = 1 << (h - l)
                irot = 1
                iimag = NTT.iroot[2]
                for s in range(1 << (l - 2)):
                    irot2 = irot * irot % P
                    irot3 = irot2 * irot % P
                    offset = s << (h - l + 2)
                    for i in range(p):
                        a0 = a[i + offset]
                        a1 = a[i + offset + p]
                        a2 = a[i + offset + 2 * p]
                        a3 = a[i + offset + 3 * p]
                        a2na3iimag = (a2 - a3) * iimag % P
                        a[i + offset] = (a0 + a1 + a2 + a3) % P
                        a[i + offset + p] = ((a0 - a1 + a2na3iimag) * irot) % P
                        a[i + offset + 2 * p] = ((a0 + a1 - a2 - a3) * irot2) % P
                        a[i + offset + 3 * p] = ((a0 - a1 - a2na3iimag) * irot3) % P
                    if s + 1 != 1 << (l - 2):
                        irot = irot * NTT.irate3[bsf(~s)] % P
                l -= 2
    
    @staticmethod
    def convolution(a, b):
        n = len(a)
        m = len(b)
        if not a or not b:
            return []
        if min(n, m) <= 40:
            if n < m:
                n, m = m, n
                a, b = b, a
            res = [0] * (n + m - 1)
            for i in range(n):
                for j in range(m):
                    res[i + j] += a[i] * b[j]
                    res[i + j] %= P
            return res
        z = 1 << ((n + m - 1).bit_length())
        iz = pow(z, P - 2, P)
        a += [0] * (z - n)
        b += [0] * (z - m)
        NTT.butterfly(a)
        NTT.butterfly(b)
        c = [a[i] * b[i] % P * iz % P for i in range(z)]
        NTT.butterfly_inv(c)
        return c[:n + m - 1]
def inv(f):
    assert f[0]
    n = len(f)
    ret = [pow(f[0], P - 2, P)]
    i = 1
    while i < n:
        tmp = NTT.convolution(ret[:], f[: i << 1])
        for j in range(len(tmp)):
            if j == 0:
                tmp[j] = (2 - tmp[j]) % P
            else:
                tmp[j] = -tmp[j] % P
        ret = NTT.convolution(ret, tmp)[: i << 1]
        i <<= 1
    return ret[:n]
n, m = map(int, input().split())
f = [0] * (n + 1)
f[1] = 1
for i in range(2, n + 1):
    f[i] = (f[i - 1] - f[i - 2]) % P
for i in range(1, n + 1):
    f[i] = f[i] * (max(0, m - i + 1) % P) % P
f[0] = 1
for i in range(1, n + 1):
    f[i] = -f[i] % P
print(inv(f)[n] % P)
 
 
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結果

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