C. Convolution
time limit per test
1 second
memory limit per test
256 megabytes
input
standard input
output
standard output

Given two sequences $$$a_0,a_1,\dots,a_{n-1}$$$ and $$$b_0,b_1,\dots,b_{m-1}$$$, the sequence $$$c_0,c_1,\dots,c_{n+m-2}$$$ is defined as follows:

$$$$$$ c_k = \sum_{i+j=k} a_i b_j .$$$$$$

Your task is to find the value of $$$$$$ \sum_{k=0}^{n+m-2} c_k. $$$$$$

Input

The first line of input contains two integers $$$n$$$ and $$$m$$$ ($$$1 \le n, m \le 10^5$$$).

The second line of input contains $$$n$$$ integers $$$a_0,a_1,\dots,a_{n-1}$$$ ($$$0 \le a_i \le 10^4$$$).

The third line of input contains $$$m$$$ integers $$$b_0,b_1,\dots,b_{m-1}$$$ ($$$0 \le b_i \le 10^4$$$).

Output

Print one integer — the value described above.

Example
Input
4 5
2 1 3 7
4 2 0 6 9
Output
273