CSES - Aalto Competitive Programming 2024 - wk9 - Mon - String padding

Time limit: 1.00 s
Memory limit: 512 MB

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:

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

Example 2