The Traveler

You are a traveler journeying along the JOI Road. The JOI Road is a straight road running east to west, and there are $n$ post towns along it. The post towns are numbered from $1$ to $n$ in order from west to east: post town $1$ is the westernmost and post town $n$ is the easternmost.

Starting from post town $1$, you set out on a journey of $m$ days. Your itinerary follows a sequence $a_1, a_2, \ldots, a_m$, where each $a_i$ is a nonzero integer describing your move on day $i$. If you begin day $i$ at post town $k$, then on day $i$ you travel in a straight line from post town $k$ to post town $k + a_i$.

Given the number of post towns $n$, the number of days $m$, the distances between adjacent post towns, and the movement sequence $a_1, a_2, \ldots, a_m$, write a program that computes the total distance you travel over the $m$ days, taken modulo $100000 = 10^5$.

The first line contains two integers $n$ and $m$, separated by a space. Here $n$ ($2 \le n \le 100000 = 10^5$) is the number of post towns along the JOI Road, and $m$ ($1 \le m \le 100000 = 10^5$) is the number of days of the journey.

Each of the next $n - 1$ lines gives a distance between adjacent post towns: line $i + 1$ ($1 \le i \le n - 1$) contains a positive integer $s_i$ ($1 \le s_i \le 100$), the distance between post town $i$ and post town $i + 1$.

Each of the next $m$ lines gives one element of the movement sequence: line $i + n$ ($1 \le i \le m$) contains the nonzero integer $a_i$ describing your move on day $i$.

It is guaranteed that you never move west of post town $1$ or east of post town $n$.

Output a single line containing the total distance you travel over the $m$ days, taken modulo $100000 = 10^5$.

For the first sample: on day $1$ you move from post town $1$ to post town $3$; on day $2$ from post town $3$ to post town $2$; on day $3$ from post town $2$ to post town $5$; on day $4$ from post town $5$ to post town $7$; and on day $5$ from post town $7$ to post town $4$. The total distance over the $5$ days is $18$.