A string ~S~ consisting of ~N~ lowercase latin characters is hashed using the following method:

$$\displaystyle hash(S) = \displaystyle \left( \sum_{i=1}^N S_i \times B^i \right) \bmod P$$

~S_i~ is the ASCII value of the ~i^\text{th}~ (one-indexed) character of string ~S~. ~B~ and ~P~ are values given to you.

Given a string ~S~, and integers ~B~ and ~P~, can you calculate ~hash(S)~?

Input Specification

The first line will contain the integer ~N~ ~(1 \le N \le 10^5)~.

The second line will contain the string ~S~ of length ~N~. ~S~ will only contain lowercase latin characters.

The third line will contain the integers ~B~ and ~P~ ~(1 \le B, P \le 10^9)~.

Output Specification

Output ~hash(S)~.

Sample Input

3
aaa
2 1

Sample Output

0