結果

問題 No.3006 ベイカーの問題
ユーザー Mao-beta
提出日時 2025-02-03 15:39:59
言語 PyPy3
(7.3.15)
結果
WA  
実行時間 -
コード長 2,269 bytes
コンパイル時間 576 ms
コンパイル使用メモリ 82,588 KB
実行使用メモリ 58,516 KB
最終ジャッジ日時 2025-02-03 15:40:04
合計ジャッジ時間 3,302 ms
ジャッジサーバーID
（参考情報） 		judge3 / judge4
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ファイルパターン 結果
sample AC * 3
other AC * 22 WA * 2
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ソースコード

diff #
プレゼンテーションモードにする

import sys
import math
import bisect
from heapq import heapify, heappop, heappush
from collections import deque, defaultdict, Counter
from functools import lru_cache
from itertools import accumulate, combinations, permutations, product
sys.set_int_max_str_digits(10 ** 6)
sys.setrecursionlimit(1000000)
MOD = 10 ** 9 + 7
MOD99 = 998244353
input = lambda: sys.stdin.readline().strip()
NI = lambda: int(input())
NMI = lambda: map(int, input().split())
NLI = lambda: list(NMI())
SI = lambda: input()
SMI = lambda: input().split()
SLI = lambda: list(SMI())
EI = lambda m: [NLI() for _ in range(m)]
# 行列積（任意サイズ）
def mul_matrix(A, B, mod=998244353):
    Ah = len(A)
    Aw = len(A[0])
    Bh = len(B)
    Bw = len(B[0])
    assert Aw == Bh
    C = [[0] * Bw for _ in range(Ah)]
    for h in range(Ah):
        Arow = A[h]
        Crow = C[h]
        for i in range(Aw):
            a = Arow[i]
            Brow = B[i]
            for w in range(Bw):
                Crow[w] = (Crow[w] + a * Brow[w]) % mod
    return C
# 正方行列の累乗 mod
def pow_matrix(A, n, mod=998244353):
    assert len(A) == len(A[0])
    bitn = len(bin(n)) - 2
    pows = []
    size = len(A)
    E = [[0] * size for _ in range(size)]
    for i in range(size):
        E[i][i] = 1
    pows.append(A)
    ans = E
    for i in range(bitn):
        if (n >> i) & 1:
            ans = mul_matrix(pows[-1], ans, mod)
        pows.append(mul_matrix(pows[-1], pows[-1], mod))
    return ans
def main():
    X1, Y1, N = NMI()
    if X1 == Y1 == 0:
        print(X1, Y1)
        return
    if X1 == 1 and Y1 == 0:
        print(N%MOD99, 0)
        return 
    A = [[X1, -5*Y1],
         [Y1, X1]]
    # (XN, YN)T = A^(N-1) * (X1, Y1)T
    # A^(N-1)+...+A^0 = (A^N - E) * (A-E)^-1
    X = pow_matrix(A, N, MOD99)
    XE = [[X[0][0]-1, X[0][1]],
          [X[1][0], X[1][1]-1]]
    AE = [[X1-1, -5*Y1],
          [Y1, X1-1]]
    d = AE[0][0]*AE[1][1]-AE[0][1]*AE[1][0]
    dinv = pow(d, MOD99-2, MOD99)
    AEinv = [[AE[1][1]*dinv, -AE[0][1]*dinv],
             [-AE[1][0]*dinv, AE[0][0]*dinv]]
    X = mul_matrix(XE, AEinv, MOD99)
    x = X[0][0] * X1 + X[0][1] * Y1
    y = X[1][0] * X1 + X[1][1] * Y1
    print(x%MOD99, y%MOD99)
if __name__ == "__main__":
    main()
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