Problem Statement

Polynomials $F(x)$ and $G(x)$ with non-negative integer coefficients are given as input.

Compute each coefficient of the polynomial $F(x) G(x)$, which has non-negative integer coefficients, modulo $258280327$.

Input

The input is given from standard input in $4$ lines in the following format:

• Line $1$ contains the degree $N$ of $F$.
• Line $2$ contains, for each non-negative integer $i$ not exceeding $N$, the coefficient $F_i$ of the degree-$i$ term of $F$, in increasing order of $i$, separated by single-byte spaces.
• Line $3$ contains the degree $M$ of $G$.
• Line $4$ contains, for each non-negative integer $j$ not exceeding $M$, the coefficient $G_j$ of the degree-$j$ term of $G$, in increasing order of $j$, separated by single-byte spaces.

Here, the degree of the zero polynomial is defined to be $0$.

Constraints

The input satisfies the following constraints:

• $N$ is an integer satisfying $0 \leq N \leq 2 \times 10^5$
• For any non-negative integer $i$ not exceeding $N$:
• if $i = N \neq 0$, then $F_i$ is an integer satisfying $0 < F_i \leq 10^{18}$
• otherwise, $F_i$ is an integer satisfying $0 \leq F_i \leq 10^{18}$
• $M$ is an integer satisfying $0 \leq M \leq 2 \times 10^5$
• For any non-negative integer $j$ not exceeding $M$:
• if $j = M \neq 0$, then $G_j$ is an integer satisfying $0 < G_j \leq 10^{18}$
• otherwise, $G_j$ is an integer satisfying $0 \leq G_j \leq 10^{18}$

Output

Output $2$ lines to standard output in the following format:

• On line $1$, output the degree $L$ of $F(x) G(x)$.
• On line $2$, output, for each non-negative integer $k$ not exceeding $L$, the coefficient of the degree-$k$ term of $F(x) G(x)$ modulo $258280327$, in increasing order of $k$, separated by single-byte spaces.

Print a newline at the end.

Sample

1
0 1
1
0 1

2
0 0 1

1
50000 7
1
1 20000

2
50000 225159026 140000

1
65536 1
1
1 15232

2
65536 223403372 15232