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 Python (3.8.2) (judge verdict: Time Limit Exceeded)

from scipy.special import comb

mod = 10 ** 9 + 7

K = int(input())
S = str(input())
len_s = len(S)

answer = 0
for i in range(K + 1):
    answer += pow(25, K-i, mod) * pow(26, i, mod) * comb(K-i+len_s-1, len_s - 1, exact=True)
    answer = answer % mod
print(answer)