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)

mod=10**9+7
k=int(input())
s=input()
n=len(s)
c=1
t=1
ans=0
m=10**20
for i in range(k+1):
  ans+=c*t
  if ans>m:ans%=mod
  c*=(n+k-i)*pow(i+1,mod-2,mod)
  if c>m:c%=mod
  t*=25
  if t>m:t%=mod
print(ans%mod)