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: Runtime Error)

#include <bits/stdc++.h>

using namespace std;
typedef long long int ll;
typedef pair<int, int> ii;

struct fastio {
    fastio() {
        ios::sync_with_stdio(false);
        cout << setprecision(10) << fixed;
        cin.tie(0);
    }
};

fastio _fast_io;

const int mod = 1e9 + 7;
int k;
string s;
const int N = 1e6 + 1;
ll fac[N];
ll inv[N];

ll power(ll a, ll b) {
    ll res = 1;
    while (b) {
        if (b & 1) {
            res = (res * a) % mod;
        }
        a = a * a % mod;
        b >>= 1;
    }
    return res;
}

void init() {
    fac[0] = 1;
    for (int i = 1; i < N; ++i) {
        fac[i] = fac[i - 1] * i % mod;
    }
    inv[N - 1] = power(fac[N - 1], mod - 2);
    for (int i = N - 2; i >= 0; --i) {
        inv[i] = inv[i + 1] * (i + 1) % mod;
    }
}

ll C(ll a, ll b) {
    return fac[a] * inv[b] % mod * inv[a - b] % mod;
}

int main() {
    init();
    cin >> k >> s;
    int n = s.length();
    ll res = 0;
    ll sum = k + n;
    for (int i = 0; i <= k; ++i) {
        res = (res + power(26, i) * C(sum - 1 - i, n - 1)
                % mod * power(25, k - i) % mod) % mod;
    }
    cout << res << endl;
    return 0;
}