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)

import sys
import math
import collections

sys.setrecursionlimit(10 ** 8)

input = sys.stdin.readline


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

    MOD = 10 ** 9 + 7

    fact = [1, 1]
    factinv = [1, 1]
    inv = [0, 1]

    def cmb(n, k, p):
        if (k < 0) or (n < k):
            return 0
        r = min(k, n - k)
        return fact[n] * factinv[k] * factinv[n - k] % p

    N = 10 ** 6
    for i in range(2, N + 1):
        fact.append((fact[-1] * i) % MOD)
        inv.append((-inv[MOD % i] * (MOD // i)) % MOD)
        factinv.append((factinv[-1] * inv[-1]) % MOD)

    ans = 0
    for i in range(K + 1):
        ans += pow(25, i, MOD) * cmb(i + len(S) - 1, len(S) - 1, MOD) * pow(26, K - i, MOD)

    print(ans % MOD)


if __name__ == '__main__':
    main()