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: Runtime Error)

K=int(input())
s=input()
S=len(s)
mod=10**9+7
MAX_N=10**6
fact=[1]
fact_inv=[0]*(MAX_N+4)
for i in range(MAX_N+3):
  fact.append(fact[-1]*(i+1)%mod)

fact_inv[-1]=pow(fact[-1],mod-2,mod)
for i in range(MAX_N+2,-1,-1):
  fact_inv[i]=fact_inv[i+1]*(i+1)%mod

def mod_comb_k(n,k,mod):
  return fact[n]*fact_inv[k]%mod*fact_inv[n-k] %mod

cnt=0
for i in range(K+1):
  a=(pow(26,i,mod)*pow(25,K-i,mod))*(mod_comb_k(K+S-i-1,S-1,mod))
  a%=mod
  cnt+=a
  cnt%=mod
print(cnt)