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 C++ (GCC 9.2.1) (judge verdict: Accepted)

#include<bits/stdc++.h>

int main(){
    using namespace std;
    constexpr unsigned long MOD = 1000000007;
    unsigned long K;
    cin >> K;
    string S;
    cin >> S;
    const auto& modpow = [](unsigned long a, unsigned long n, unsigned long b = 1) -> unsigned long {
        unsigned long r{b % MOD};
        while(n){
            if(n & 1)(r *= a) %= MOD;
            (a *= a) %= MOD;
            n >>= 1;
        }
        return r;
    };
    unsigned long N{S.size()};
    unsigned long ans{0}, coef{modpow(26, K)}, den{1}, num{1};
    for(unsigned long i{0}; i <= K; ++i){
        ans += modpow(den, MOD - 2, num * coef);
        (coef *= 423076927) %= MOD;
        (den *= (i + 1)) %= MOD;
        (num *= (N + i)) %= MOD;
    }
    cout << ans % MOD << endl;
    return 0;
}