271. Multiply Polynomials

I'm a slow walker, but I never walk backwards.

Task Description

Write a program to multiply two polynomials. We will represent a polynomial by a sequence of its coefficients. For example, we will use $(1, 2, 3)$ to represent $x^2 + 2x + 3$, and $(4, 5, 6, 7)$ for $4 x^3 + 5 x^2 + 6x + 7$.

Limits

The number of coefficients in a polynomial is no more than 100. The coefficients are positive and no more than 100.

Input

There are four lines in the input. The first line is a positive integer $n$, the number of coefficients of the first polynomial $f(x)$. The second line has $m$ integers for the coefficients of the second polynomial $g(x)$. Similarly the third line and fourth line are for the second polynomial.

Output

The coefficients of the product of the two input polynomials $f(x)g(x)$.

Sample input

3
1 2 3
4
4 5 6 7

Sample output

4 13 28 34 32 21

Discussion