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

k = int(input())
s = input()
slen = len(s)
md = 10 ** 9 + 7

ans = 0
dict = {}
for i in range(k+1):
    now = pow(26, k-i, md) * pow(25, i, md)
    key = (i+slen-1, slen-1)
    ret = dict.get(key)
    if not ret:
        ret = comb(key[0], key[1], exact=True)
        dict[key] = ret
    now *= ret
    ans = (ans + now) % md
print(ans)