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)

import sys

def input():
    return sys.stdin.readline().strip()

def main():
    K = int(input())
    S = input()

    mod = 10 ** 9 + 7
    n = len(S)
    ans = 0

    fact =[1]*(K+n)
    factinv = [1]*(K+n)


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

    def nCr(n,r):
        return (fact[n] * factinv[r] * factinv[n-r]) % mod

    for i in range(K+1):
        ans += ((25 ** i * nCr(i+n-1,n-1)) * (26 ** (K - i))) % mod
    print(ans)

if __name__ == "__main__":
    main()