Required Substring

Your task is to calculate the number of strings of length n having a given pattern of length m as their substring. All strings consist of characters A–Z.

Input

The first input line has an integer n: the length of the final string. The second line has a pattern of length m.

Output

Print the number of strings modulo 10^9+7.

Constraints

$1 \le n \le 1000$

$1 \le m \le 100$

Example

Input

6
ABCDB

Output

52

Explanation: The final string will be of the form ABCDBx or xABCDB where x is any character between A–Z.