Problem:
Score: 600 points

Problem Statement

How many strings can be obtained by applying the following operation on a string S exactly K times: "choose one lowercase English letter and insert it somewhere"?

The answer can be enormous, so print it modulo (10^9+7).

Constraints

K is an integer between 1 and 10^6 (inclusive).

S is a string of length between 1 and 10^6 (inclusive) consisting of lowercase English letters.

Input

Input is given from Standard Input in the following format:

K
S

Output

Print the number of strings satisfying the condition, modulo (10^9+7).

Sample Input 1

5
oof

Sample Output 1

575111451

For example, we can obtain proofend, moonwolf, and onionpuf, while we cannot obtain oofsix, oofelevennn, voxafolt, or fooooooo.

Sample Input 2

37564
whydidyoudesertme

Sample Output 2

318008117

Solution in Ruby (2.7.1) (judge verdict: Time Limit Exceeded)

END { load __FILE__ unless $stdin.eof? }

k = gets.to_i
s = gets.chomp
m = 10**9 + 7

r = Regexp.compile(s.chars.join('.*'))
puts (('a' * (s.length + k))...('a' * (s.length + k + 1))).count(&r.method(:match?)) % m