Problem G
Number Theoretic Transform

You are given two polynomials. You should simply print their product. This time you have to do it fast though and modulo $998\, 244\, 353$.

Input

The first line of input contains two positive integers $n, m$, the number of coefficients in each polynomial. The next two lines contain one polynomial each. Each polynomial is given as its coefficients in ascending order, that is to say if the input is a0 a1 a2 a3 then that represents the polynomial $a_0 + a_1 x + a_2 x^2 + a_3 x^3$. You may assume that $n, m \leq 10^5$ and that all coefficients $a_i$ satisfy $0 \leq a_i < 998\, 244\, 353$.

Output

Print the product of the two polynomials in the input in the same format as the polynomials in the input. Print exactly $n + m - 1$ coefficients of the output polynomial. Print the coefficients modulo $998\, 244\, 353$.

3 4
1 2 3
4 5 6 7

4 13 28 34 32 21 

3 3
10000000 10000000 10000000
10000000 10000000 10000000

871938225 745632097 619325969 745632097 871938225