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 PyPy3 (7.3.0) (judge verdict: Accepted)

K=int(input())
S=input()
N=len(S)
mod=10**9+7

fact=[0]*(K+N)
fact[0]=fact[1]=1
for i in range(2,K+N):
    fact[i]=fact[i-1]*i%mod

def comb(n,r):
    ret=fact[n]*pow(fact[r],mod-2,mod)*pow(fact[n-r],mod-2,mod)%mod
    return ret

ans=0
for i in range(K+1):
    ans+=pow(26,i,mod)*pow(25,K-i,mod)*comb(K+N-1-i,N-1)
    ans%=mod

print(ans)