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 ABCDB$x$ or $x$ABCDB where $x$ is any character between A–Z.