- Time limit: 1.00 s
- Memory limit: 512 MB
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.