結果

問題 No.3044 よくあるカエルさん
ユーザー lif4635
提出日時 2025-02-28 22:19:35
言語 PyPy3
(7.3.15)
結果
RE  
実行時間 -
コード長 16,961 bytes
コンパイル時間 267 ms
コンパイル使用メモリ 82,224 KB
実行使用メモリ 77,976 KB
最終ジャッジ日時 2025-02-28 22:19:38
合計ジャッジ時間 2,958 ms
ジャッジサーバーID
（参考情報） 		judge2 / judge1
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 * 1
other WA * 3 RE * 17
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

# input
import sys
input = sys.stdin.readline
II = lambda : int(input())
MI = lambda : map(int, input().split())
LI = lambda : [int(a) for a in input().split()]
SI = lambda : input().rstrip()
LLI = lambda n : [[int(a) for a in input().split()] for _ in range(n)]
LSI = lambda n : [input().rstrip() for _ in range(n)]
MI_1 = lambda : map(lambda x:int(x)-1, input().split())
LI_1 = lambda : [int(a)-1 for a in input().split()]
def graph(n:int, m:int, dir:bool=False, index:int=-1) -> list[set[int]]:
    edge = [set() for i in range(n+1+index)]
    for _ in range(m):
        a,b = map(int, input().split())
        a += index
        b += index
        edge[a].add(b)
        if not dir:
            edge[b].add(a)
    return edge
def graph_w(n:int, m:int, dir:bool=False, index:int=-1) -> list[set[tuple]]:
    edge = [set() for i in range(n+1+index)]
    for _ in range(m):
        a,b,c = map(int, input().split())
        a += index
        b += index
        edge[a].add((b,c))
        if not dir:
            edge[b].add((a,c))
    return edge
mod = 998244353
inf = 1001001001001001001
ordalp = lambda s : ord(s)-65 if s.isupper() else ord(s)-97
ordallalp = lambda s : ord(s)-39 if s.isupper() else ord(s)-97
yes = lambda : print("Yes")
no = lambda : print("No")
yn = lambda flag : print("Yes" if flag else "No")
def acc(a:list[int]):
    sa = [0]*(len(a)+1)
    for i in range(len(a)):
        sa[i+1] = a[i] + sa[i]
    return sa
prinf = lambda ans : print(ans if ans < 1000001001001001001 else -1)
alplow = "abcdefghijklmnopqrstuvwxyz"
alpup = "ABCDEFGHIJKLMNOPQRSTUVWXYZ"
alpall = "abcdefghijklmnopqrstuvwxyzABCDEFGHIJKLMNOPQRSTUVWXYZ"
URDL = {'U':(-1,0), 'R':(0,1), 'D':(1,0), 'L':(0,-1)}
DIR_4 = [[-1,0],[0,1],[1,0],[0,-1]]
DIR_8 = [[-1,0],[-1,1],[0,1],[1,1],[1,0],[1,-1],[0,-1],[-1,-1]]
DIR_BISHOP = [[-1,1],[1,1],[1,-1],[-1,-1]]
prime60 = [2,3,5,7,11,13,17,19,23,29,31,37,41,43,47,53,59]
sys.set_int_max_str_digits(0)
# sys.setrecursionlimit(10**6)
# import pypyjit
# pypyjit.set_param('max_unroll_recursion=-1')
from collections import defaultdict
from heapq import heappop,heappush
from bisect import bisect_left,bisect_right
DD = defaultdict
BSL = bisect_left
BSR = bisect_right
MOD = 998244353
_IMAG = 911660635
_IIMAG = 86583718
_rate2 = (0, 911660635, 509520358, 369330050, 332049552, 983190778, 123842337, 238493703, 975955924, 603855026, 856644456, 131300601, 842657263, 
    730768835, 942482514, 806263778, 151565301, 510815449, 503497456, 743006876, 741047443, 56250497, 867605899, 0)
_irate2 = (0, 86583718, 372528824, 373294451, 645684063, 112220581, 692852209, 155456985, 797128860, 90816748, 860285882, 927414960, 354738543, 
    109331171, 293255632, 535113200, 308540755, 121186627, 608385704, 438932459, 359477183, 824071951, 103369235, 0)
_rate3 = (0, 372528824, 337190230, 454590761, 816400692, 578227951, 180142363, 83780245, 6597683, 70046822, 623238099, 183021267, 402682409, 
    631680428, 344509872, 689220186, 365017329, 774342554, 729444058, 102986190, 128751033, 395565204, 0)
_irate3 = (0, 509520358, 929031873, 170256584, 839780419, 282974284, 395914482, 444904435, 72135471, 638914820, 66769500, 771127074, 985925487, 
    262319669, 262341272, 625870173, 768022760, 859816005, 914661783, 430819711, 272774365, 530924681, 0)
def _fft(a):
    n = len(a)
    h = (n - 1).bit_length()
    le = 0
    for le in range(0, h - 1, 2):
        p = 1 << (h - le - 2)
        rot = 1
        for s in range(1 << le):
            rot2 = rot * rot % MOD
            rot3 = rot2 * rot % 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) % MOD * _IMAG
                a[i + offset] = (a0 + a2 + a1 + a3) % MOD
                a[i + offset + p] = (a0 + a2 - a1 - a3) % MOD
                a[i + offset + p * 2] = (a0 - a2 + a1na3imag) % MOD
                a[i + offset + p * 3] = (a0 - a2 - a1na3imag) % MOD
            rot = rot * _rate3[(~s & -~s).bit_length()] % MOD
    if h - le & 1:
        rot = 1
        for s in range(1 << (h - 1)):
            offset = s << 1
            l = a[offset]
            r = a[offset + 1] * rot
            a[offset] = (l + r) % MOD
            a[offset + 1] = (l - r) % MOD
            rot = rot * _rate2[(~s & -~s).bit_length()] % MOD
def _ifft(a):
    n = len(a)
    h = (n - 1).bit_length()
    le = h
    for le in range(h, 1, -2):
        p = 1 << (h - le)
        irot = 1
        for s in range(1 << (le - 2)):
            irot2 = irot * irot % MOD
            irot3 = irot2 * irot % 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) * _IIMAG % MOD
                a[i + offset] = (a0 + a1 + a2 + a3) % MOD
                a[i + offset + p] = (a0 - a1 + a2na3iimag) * irot % MOD
                a[i + offset + p * 2] = (a0 + a1 - a2 - a3) * irot2 % MOD
                a[i + offset + p * 3] = (a0 - a1 - a2na3iimag) * irot3 % MOD
            irot = irot * _irate3[(~s & -~s).bit_length()] % MOD
    if le & 1:
        p = 1 << (h - 1)
        for i in range(p):
            l = a[i]
            r = a[i + p]
            a[i] = l + r if l + r < MOD else l + r - MOD
            a[i + p] = l - r if l - r >= 0 else l - r + MOD
def ntt(a):
    if len(a) <= 1: return
    _fft(a)
def intt(a):
    if len(a) <= 1: return
    _ifft(a)
    iv = pow(len(a), MOD - 2, MOD)
    for i, x in enumerate(a): a[i] = x * iv % MOD
def multiply(s: list, t: list) -> list:
    n, m = len(s), len(t)
    l = n + m - 1
    if min(n, m) <= 60:
        a = [0] * l
        for i, x in enumerate(s):
            for j, y in enumerate(t):
                a[i + j] += x * y
        return [x % MOD for x in a]
    z = 1 << (l - 1).bit_length()
    a = s + [0] * (z - n)
    b = t + [0] * (z - m)
    _fft(a)
    _fft(b)
    for i, x in enumerate(b): a[i] = a[i] * x % MOD
    _ifft(a)
    a[l:] = []
    iz = pow(z, MOD - 2, MOD)
    return [x * iz % MOD for x in a]
def pow2(s: list) -> list:
    n = len(s)
    l = (n << 1) - 1
    if n <= 60:
        a = [0] * l
        for i, x in enumerate(s):
            for j, y in enumerate(s):
                a[i + j] += x * y
        return [x % MOD for x in a]
    z = 1 << (l - 1).bit_length()
    a = s + [0] * (z - n)
    _fft(a)
    for i, x in enumerate(a): a[i] = x * x % MOD
    _ifft(a)
    a[l:] = []
    iz = pow(z, MOD - 2, MOD)
    return [x * iz % MOD for x in a]
def ntt_doubling(a: list) -> None:
    M = len(a)
    b = a[:]
    intt(b)
    r = 1
    zeta = pow(3, (MOD - 1) // (M << 1), MOD)
    for i, x in enumerate(b):
        b[i] = x * r % MOD
        r = r * zeta % MOD
    ntt(b)
    a += b
def mod_sqrt(a: int, p: int):
    'x s.t. x**2 == a (mod p) if exist else -1'
    if a < 2: return a
    if pow(a, (p - 1) >> 1, p) != 1: return -1
    b = 1
    while pow(b, (p - 1) >> 1, p) == 1: b += 1
    m = p - 1; e = 0
    while not m & 1:
        m >>= 1
        e += 1
    x = pow(a, (m - 1) >> 1, p)
    y = (a * x % p) * x % p
    x = a * x % p
    z = pow(b, m, p)
    while y != 1:
        j = 0
        t = y
        while t != 1:
            j += 1
            t = t * t % p
        z = pow(z, 1 << (e - j - 1), p)
        x = x * z % p
        z = z * z % p
        y = y * z % p
        e = j
    return x
from math import log2
# https://nyaannyaan.github.io/library/fps/formal-power-series.hpp
def fps_add(a: list, b: list) -> list:
    if len(a) < len(b):
        res = b[::]
        for i, x in enumerate(a): res[i] += x
    else:
        res = a[::]
        for i, x in enumerate(b): res[i] += x
    return [x % MOD for x in res]
def fps_add_scalar(a: list, k: int) -> list:
    res = a[:]
    res[0] = (res[0] + k) % MOD
    return res
def fps_sub(a: list, b: list) -> list:
    if len(a) < len(b):
        res = b[::]
        for i, x in enumerate(a): res[i] -= x
        res = fps_neg(res)
    else:
        res = a[::]
        for i, x in enumerate(b): res[i] -= x
    return [x % MOD for x in res]
def fps_sub_scalar(a: list, k: int) -> list:
    return fps_add_scalar(a, -k)
def fps_neg(a: list) -> list:
    return [MOD - x if x else 0 for x in a]
def fps_mul_scalar(a: list, k: int) -> list:
    return [x * k % MOD for x in a]
def fps_matmul(a: list, b: list) -> list:
    'not verified'
    return [x * b[i] % MOD for i, x in enumerate(a)]
def fps_div(a: list, b: list) -> list:
    if len(a) < len(b): return []
    n = len(a) - len(b) + 1
    cnt = 0
    if len(b) > 64:
        return multiply(a[::-1][:n], fps_inv(b[::-1], n))[:n][::-1]
    f, g = a[::], b[::]
    while g and not g[-1]:
        g.pop()
        cnt += 1
    coef = pow(g[-1], MOD - 2, MOD)
    g = fps_mul_scalar(g, coef)
    deg = len(f) - len(g) + 1
    gs = len(g)
    quo = [0] * deg
    for i in range(deg)[::-1]:
        quo[i] = x = f[i + gs - 1] % MOD
        for j, y in enumerate(g):
            f[i + j] -= x * y
    return fps_mul_scalar(quo, coef) + [0] * cnt
def fps_mod(a: list, b: list) -> list:
    res = fps_sub(a, multiply(fps_div(a, b),  b))
    while res and not res[-1]: res.pop()
    return res
def fps_divmod(a: list, b: list):
    q = fps_div(a, b)
    r = fps_sub(a, multiply(q, b))
    while r and not r[-1]: r.pop()
    return q, r
def fps_eval(a: list, x: int) -> int:
    r = 0; w = 1
    for v in a:
        r += w * v % MOD
        w = w * x % MOD
    return r % MOD
def fps_inv(a: list, deg: int=-1) -> list:
    # assert(self[0] != 0)
    if deg == -1: deg = len(a)
    res = [0] * deg
    res[0] = pow(a[0], MOD - 2, MOD)
    d = 1
    while d < deg:
        f = [0] * (d << 1)
        tmp = min(len(a), d << 1)
        f[:tmp] = a[:tmp]
        g = [0] * (d << 1)
        g[:d] = res[:d]
        ntt(f)
        ntt(g)
        for i, x in enumerate(g): f[i] = f[i] * x % MOD
        intt(f)
        f[:d] = [0] * d
        ntt(f)
        for i, x in enumerate(g): f[i] = f[i] * x % MOD
        intt(f)
        for j in range(d, min(d << 1, deg)):
            if f[j]: res[j] = MOD - f[j]
            else: res[j] = 0
        d <<= 1
    return res
def fps_pow(a: list, k: int, deg=-1) -> list:
    n = len(a)
    if deg == -1: deg = n
    if k == 0:
        if not deg: return []
        ret = [0] * deg
        ret[0] = 1
        return ret
    for i, x in enumerate(a):
        if x:
            rev = pow(x, MOD - 2, MOD)
            ret = fps_mul_scalar(fps_exp(fps_mul_scalar(fps_log(fps_mul_scalar(a, rev)[i:], deg),  k), deg), pow(x, k, MOD))
            ret[:0] = [0] * (i * k)
            if len(ret) < deg:
                ret[len(ret):] = [0] * (deg - len(ret))
                return ret
            return ret[:deg]
        if (i + 1) * k >= deg: break
    return [0] * deg
def fps_exp(a: list, deg=-1) -> list:
    # assert(not self or self[0] == 0)
    if deg == -1: deg = len(a)
    inv = [0, 1]
    def inplace_integral(F: list) -> list:
        n = len(F)
        while len(inv) <= n:
            j, k = divmod(MOD, len(inv))
            inv.append((-inv[k] * j) % MOD)
        return [0] + [x * inv[i + 1] % MOD for i, x in enumerate(F)]
    def inplace_diff(F: list) -> list:
        return [x * i % MOD for i, x in enumerate(F) if i]
    b = [1, (a[1] if 1 < len(a) else 0)]
    c = [1]
    z1 = []
    z2 = [1, 1]
    m = 2
    while m < deg:
        y = b + [0] * m
        ntt(y)
        z1 = z2
        z = [y[i] * p % MOD for i, p in enumerate(z1)]
        intt(z)
        z[:m >> 1] = [0] * (m >> 1)
        ntt(z)
        for i, p in enumerate(z1): z[i] = z[i] * (-p) % MOD
        intt(z)
        c[m >> 1:] = z[m >> 1:]
        z2 = c + [0] * m
        ntt(z2)
        tmp = min(len(a), m)
        x = a[:tmp] + [0] * (m - tmp)
        x = inplace_diff(x)
        x.append(0)
        ntt(x)
        for i, p in enumerate(x): x[i] = y[i] * p % MOD
        intt(x)
        for i, p in enumerate(b):
            if not i: continue
            x[i - 1] -= p * i % MOD
        x += [0] * m
        for i in range(m - 1): x[m + i], x[i] = x[i], 0
        ntt(x)
        for i, p in enumerate(z2): x[i] = x[i] * p % MOD
        intt(x)
        x.pop()
        x = inplace_integral(x)
        x[:m] = [0] * m
        for i in range(m, min(len(a), m << 1)): x[i] += a[i]
        ntt(x)
        for i, p in enumerate(y): x[i] = x[i] * p % MOD
        intt(x)
        b[m:] = x[m:]
        m <<= 1
    return b[:deg]
def fps_log(a: list, deg=-1) -> list:
    # assert(a[0] == 1)
    if deg == -1: deg = len(a)
    return fps_integral(multiply(fps_diff(a), fps_inv(a, deg))[:deg - 1])
def fps_integral(a: list) -> list:
    n = len(a)
    res = [0] * (n + 1)
    if n: res[1] = 1
    for i in range(2, n + 1):
        j, k = divmod(MOD, i)
        res[i] = (-res[k] * j) % MOD
    for i, x in enumerate(a): res[i + 1] = res[i + 1] * x % MOD
    return res
def fps_diff(a: list) -> list:
    return [i * x % MOD for i, x in enumerate(a) if i]
def shrink(a: list) -> None:
    while a and not a[-1]: a.pop()
class Mat:
    def __init__(self, a00: list, a01: list, a10: list, a11: list) -> None:
        self.arr = [a00, a01, a10, a11]
    def __mul__(self, r):
        a00, a01, a10, a11 = self.arr
        if type(r) is Mat:
            ra00, ra01, ra10, ra11 = r.arr
            A00 = fps_add(multiply(a00, ra00), multiply(a01, ra10))
            A01 = fps_add(multiply(a00, ra01), multiply(a01, ra11))
            A10 = fps_add(multiply(a10, ra00), multiply(a11, ra10))
            A11 = fps_add(multiply(a10, ra01), multiply(a11, ra11))
            shrink(A00)
            shrink(A01)
            shrink(A10)
            shrink(A11)
            return Mat(A00, A01, A10, A11)
        b0 = fps_add(multiply(a00, r[0]), multiply(a01, r[1]))
        b1 = fps_add(multiply(a10, r[0]), multiply(a11, r[1]))
        shrink(b0)
        shrink(b1)
        return [b0, b1]
    @staticmethod
    def I(): return Mat([1], [], [], [1])        
def inner_naive_gcd(m: Mat, p: list) -> None:
    quo, rem = fps_divmod(p[0], p[1])
    b10 = fps_sub(m.arr[0], multiply(m.arr[2], quo))
    b11 = fps_sub(m.arr[1], multiply(m.arr[3], quo))
    shrink(rem)
    shrink(b10)
    shrink(b11)
    m.arr = [m.arr[2], m.arr[3], b10, b11]
    p[0], p[1] = p[1], rem
def inner_half_gcd(p: list) -> Mat:
    n = len(p[0]); m = len(p[1])
    k = n + 1 >> 1
    if m <= k: return Mat.I()
    m1 = inner_half_gcd([p[0][k:], p[1][k:]])
    p = m1 * p
    if len(p[1]) <= k: return m1
    inner_naive_gcd(m1, p)
    if len(p[1]) <= k: return m1
    l = len(p[0]) - 1
    j = 2 * k - l
    p[0] = p[0][j:]
    p[1] = p[1][j:]
    return inner_half_gcd(p) * m1
def inner_poly_gcd(a: list, b: list) -> Mat:
    p = [a[::], b[::]]
    shrink(p[0]); shrink(p[1])
    n = len(p[0]); m = len(p[1])
    if n < m:
        mat = inner_poly_gcd(p[1], p[0])
        mat.arr = [mat.arr[1], mat.arr[0], mat.arr[2], mat.arr[3]]
        return mat
    
    res = Mat.I()
    while 1:
        m1 = inner_half_gcd(p)
        p = m1 * p
        if not p[1]: return m1 * res
        inner_naive_gcd(m1, p)
        if not p[1]: return m1 * res
        res = m1 * res
def poly_gcd(a: list, b: list) -> list:
    p = [a, b]
    m = inner_poly_gcd(a, b)
    p = m * p
    if p[0]:
        coef = pow(p[0][-1], MOD - 2, MOD)
        for i, x in enumerate(p[0]): p[0][i] = x * coef % MOD
    return p[0]
def poly_inv(f: list, g: list) -> list:
    p = [f, g]
    m = inner_poly_gcd(f, g)
    gcd = (m * p)[0]
    if len(gcd) != 1: return [0, []]
    x = [[1], g]
    return [1, fps_mul_scalar(fps_mod((m * x)[0], g), pow(gcd[0], MOD - 2, MOD))]
def LinearRecurrence(n: int, p: list, q: list):
    """
    [x^n]P(x)/Q(x) を求める
    deg(p) < deg(q)が必要
    """
    # assert len(p) < len(q)
    shrink(q)
    while n:
        q2 = q[:]
        for i in range(1,len(q2),2): q2[i] = (-q2[i])%MOD
        s = multiply(p,q2)
        t = multiply(q,q2)
        for i in range(n&1,len(s),2): p[i>>1] = s[i]
        for i in range(0,len(t),2): q[i>>1] = t[i]
        n >>= 1
    return p[0]%MOD
def Bostan_Mori(n: int, a: list, c: list):
    """
    k 項間漸化式を求める
    aが初項、cが漸化式の係数
    """
    # assert c[0] != 0
    k = len(c)
    if n < len(a):
        return a[n]
    c = [1] + [(-i)%MOD for i in c]
    p = multiply(a,c)[:k-1]
    return LinearRecurrence(n,p,c)
n,t = MI()
k,l = MI()
inv6 = pow(6, -1, mod)
a = [0]*t
a[0] = 1
c = [0]*(t+1)
c[1] = inv6*(k-1)%mod
c[2] = inv6*(l-k)%mod
c[t] = inv6*(6-l+1)%mod
for i in range(1,t):
    a[i] += a[i-1] * c[1]
    if i >= 2:
        a[i] += a[i-2] * c[2] 
    if i >= t:
        a[i] += a[i-t] * c[t]
    a[i] %= mod
# print(a)
res = Bostan_Mori(n-1, a, c) % mod
print(res)
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0