結果

問題 No.3182 recurrence relation’s intersection sum
ユーザー lif4635
提出日時 2025-06-13 22:24:33
言語 PyPy3
(7.3.15)
結果
TLE  
実行時間 -
コード長 5,500 bytes
コンパイル時間 416 ms
コンパイル使用メモリ 82,676 KB
実行使用メモリ 101,504 KB
最終ジャッジ日時 2025-06-13 22:24:55
合計ジャッジ時間 20,655 ms
ジャッジサーバーID
（参考情報） 		judge2 / judge1
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ファイルパターン 結果
sample AC * 3
other AC * 36 TLE * 1 -- * 3
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 # 

# 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,deque
from heapq import heappop,heappush
from bisect import bisect_left,bisect_right
DD = defaultdict
BSL = bisect_left
BSR = bisect_right


mod = 998244353

def mat_add(a, b):
    # assert len(a) == len(b)
    # assert len(a[0]) == len(b[0])
    n = len(a)
    m = len(a[0])
    res = [[0]*m for i in range(n)]
    for i in range(n):
        for j in range(m):
            res[i][j] = (a[i][j] + b[i][j])%mod
    return res

def mat_sub(a, b):
    # assert len(a) == len(b)
    # assert len(a[0]) == len(b[0])
    n = len(a)
    m = len(a[0])
    res = [[0]*m for i in range(n)]
    for i in range(n):
        for j in range(m):
            res[i][j] = (a[i][j] - b[i][j])%mod
    return res

def mat_mul(a, b):
    # assert len(a[0]) == len(b)
    n = len(a)
    m = len(b[0])
    res = [[0]*m for i in range(n)]
    for i,r_i in enumerate(res):
        for k,a_ik in enumerate(a[i]):
            for j,b_kj in enumerate(b[k]):
                r_i[j] = (r_i[j] + a_ik*b_kj)%mod
    return res

def mat_pow2(a):
    n = len(a)
    res = [[0]*n for i in range(n)]
    for i,r_i in enumerate(res):
        for k,a_ik in enumerate(a[i]):
            for j,a_kj in enumerate(a[k]):
                r_i[j] = (r_i[j] + a_ik*a_kj)%mod
    return res

def mat_inv(a, mod = mod):
    """いつか実装します"""
    pass

def mat_pow(a, exp):
    n = len(a)
    res = [[int(i == j) for j in range(n)] for i in range(n)]
    
    d = exp.bit_length()
    for i in range(d, -1, -1):
        if (exp >> i) & 1: res = mat_mul(res, a)
        if i == 0: return res
        res = mat_pow2(res)

class Comb:
    __slots__ = ["fac", "finv", "mod"]
    def __init__(self, lim:int, mod:int = mod):
        """
        mod : prime
        """
        self.fac = [1]*(lim+1)
        self.finv = [1]*(lim+1)
        self.mod = mod
        for i in range(2,lim+1):
            self.fac[i] = self.fac[i-1]*i%self.mod
        self.finv[lim] = pow(self.fac[lim],-1,mod)
        for i in range(lim,2,-1):
            self.finv[i-1] = self.finv[i]*i%self.mod
    
    def C(self, a, b):
        if b < 0: return 0
        assert b >= 0, "The second argument is negative."
        if a < b: return 0
        if a < 0: return 0
        return self.fac[a]*self.finv[b]%self.mod*self.finv[a-b]%self.mod
    
    def P(self, a, b):
        
        assert b >= 0, "The second argument is negative."
        if a < b: return 0
        if a < 0: return 0
        return self.fac[a]*self.finv[a-b]%self.mod
    
    def H(self, a, b): return self.C(a+b-1,b)
    def F(self, a): return self.fac[a]
    def Fi(self, a): return self.finv[a]
    def __call__(self, a, b): return self.C(a, b)

comb = Comb(1000)

def solve(k, x):
    d = k + 4
    
    mat = [[0] * d for i in range(d)]
    # それ以外の更新
    mat[0][0] = k
    mat[0][-2] = 1
    mat[0][-1] = 1
    
    # 累積和の更新
    mat[1][0] = 1
    mat[1][1] = 1
    
    for m in range(k + 1):
        # n ^ m の更新
        for j in range(m+1):
            mat[2+m][2+j] = comb(m, j)
    
    
    
    # k^n の更新
    mat[-1][-1] = k
    
    # for i in range(d):
    #     print(mat[i])
    
    res = mat_pow(mat, x)
    
    v = [[0] for i in range(d)]
    v[0][0] = 1
    v[2][0] = 1
    v[-1][0] = 1
    
    res = mat_mul(res, v)
    # print(res)
    return res[1][0]

# for d in range(10):
#     solve(2, d)

k, l, r = MI()
ans = (solve(k, r + 1) - solve(k, l)) % mod
print(ans)
0