A 5-way recurrence

a_n+1=1×a_n-1×b_n+2×c_n-3×d_n+5×e_n-8 b_n+1=1×b_n-2×c_n+3×d_n-5×e_n+8×a_n-13 c_n+1=2×c_n-3×d_n+5×e_n-8×a_n+13×b_n-21 d_n+1=3×d_n-5×e_n+8×a_n-13×b_n+21×c_n-34 e_n+1=5×e_n-8×a_n+13×b_n-21×c_n+34×d_n-55 a₀=b₀=c₀=d₀=e₀=1 What is n_th solution for n=3⁴⁵? Answer format: a_n%M,b_n%M,c_n%M,d_n%M,e_n%M where M=10000019 Note: The answer should consist of positive numbers.