Problem 2: A Board Game, (K Narayan Kumar, CMI)
In this task you have to determine the outcome of a board game. The board on which the game is played has N places labelled 1,2,...,N. Each position is marked with either a + or a -. The position 1 is always marked with a +.
A token is initially placed at position 1. The game proceeds as follows: In each round, a single die is thrown. Let the current position of the token be j and let the die show d. The new position of the token is determined as follows:
If the position j is labelled + and if j+d ≤ N then the token moves to j+d, otherwise it remains at j.
If the position j is labelled - and if j-d ≥ 1 then the token moves to j-d, otherwise it remains at j
The score at the end of the game is the number of times the token visits the position 1.
For example if the board looks like
1 2 3 4 5 6 7 8 9 10 11 12 + + - + - - + - - + - -
and the sequence of throws of the die is 1,1,2,3,2,6,3,2,6,2 then the sequence of positions visited by the token is 1 2 3 1 4 6 6 3 1 7 9 and the resulting score is 3.
You are given the description of the board and a sequence of throws of the die. Your aim is to determine the score at the end of the game.
Input format
The first line contains two integers N and M where N is the number of positions on the board and M is the number of throws of the die. Lines 2,...,N+1 contain a + or a -. Line i+1, 1 ≤ i ≤ N, indicates whether position i is marked with a + or a -. The next M lines, lines N+2,..., N+1+M, each contain a single integer d indicating a throw of the die, with 1 ≤ d ≤ 6.
Output format
A single integer indicating the score.
Test Data
You may assume 7 ≤ N ≤ 10000 and 1 ≤ M ≤ 10000.
Example
We now illustrate the input and output formats using the example described above.
Sample input:
12 10 + + - + - - + - - + - - 1 1 2 3 2 6 3 2 6 2
Sample output:
3
Test data: