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>
using namespace std;

template<class T>bool chmax(T &a, const T &b) { if (a<b) { a=b; return 1; } return 0; }
template<class T>bool chmin(T &a, const T &b) { if (b<a) { a=b; return 1; } return 0; }

using ll = long long;

const int dx[4] = {1, 0, -1, 0};
const int dy[4] = {0, 1, 0, -1};
const int INF = 1<<30;
const ll mod = 1000000007LL;

#define rep(i, n) for (int i = 0; i < (int)(n); i++)

ll pow(ll a, ll n, ll m) {
	ll ret = 1LL;
	for (; n > 0LL; n >>= 1LL, a = a * a % m) {
		if (n % 2LL == 1LL) {
			ret = ret * a % m;
		}
	}
	return ret;
}

int main(){
    ll K;
    string S;
    cin>>K>>S;
    ll N = S.size();
    ll ans = 0LL;
    ll t = pow(26LL,K,mod);
    ll s = 1;
    for(ll i = N-1; i < N+K; i++){
        ans= (ans + t*s)%mod;
        t = (((t*25LL)%mod)*pow(26LL,mod-2,mod))%mod;
        s = (((s * (i+1))%mod)*pow(i-N+2,mod-2,mod))%mod;
    }
    cout<<ans<<endl;
}