Description

Given a degree $n$ polynomial $F(x)$ and a degree $m$ polynomial $G(x)$, compute the product $F(x)$ and $G(x)$.

Input Format

The first line contains two integers $n, m$.

The next line contains $n+1$ integers, representing the coefficients of $F(x)$ from lowest degree to highest.

The next line contains $m+1$ integers, representing the coefficients of $G(x)$ from lowest degree to highest.

Output Format

Output one line containing $n+m+1$ integers, representing the coefficients of $F(x) \cdot G(x)$ from lowest degree to highest.

1 2
1 2
1 2 1

1 4 5 2

Hint

It is guaranteed that all input coefficients are integers between $0$ and $9$ inclusive.

For $100\%$ of the testdata: $1 \le n, m \leq {10}^6$.

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