You are given a string of length $m$ that is going to be padded with characters A-Z in both ends until it's length becomes $n$. Calculate the number of different padded strings.

Input

The first input line contains an integer $n$ shows 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

• $1 \le m \le n \le 1000$
• $1 \le m \le 100$

Example 1

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.

Example 2

Input:

100
YWANYWAZYWANYWA

Output:

134837038