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: Time Limit Exceeded)

MOD = 10**9+7
k = int(input())
s = input()
n = len(s)


def com(n, r):
    X = Y = 1
    if r < 0 or n < r:
        return 0
    if n-r < r:
        r = n-r
    for i in range(1, r+1):
        Y = Y*i % MOD
        X = X*(n-i+1) % MOD
    Y = pow(Y, MOD-2, MOD)
    return X*Y % MOD


ans = 0
for x in range(k+1):
    ans += pow(26, x, MOD)*com(n+k-x-1, n-1)*pow(25, k-x, MOD)
    ans %= MOD
print(ans)