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: Wrong Answer)

//#define _GLIBCXX_DEBUG
#include <bits/stdc++.h>
using namespace std;
#define all(v) v.begin(), v.end()
using in = int64_t;
#define rep(i, n) for (in i = 0; i < (in)(n); i++)
#define REP(i,a,b) for(in i=(in)(a);i<(in)(b);i++)
#define Yes cout<<"Yes"<<endl
#define No cout<<"No"<<endl
#define yes cout<<"yes"<<endl
#define no cout<<"no"<<endl
const double PI=3.14159265358979323846;
const in MOD = 1000000007;
const in INF=1e18+7;
const in inf=1e9+7;
using P=pair<in,in>;
vector<in> dx={0,1,-1,0};
vector<in> dy={1,0,0,-1};


int main(){
ios::sync_with_stdio(0); cin.tie(0); cout.tie(0);
cout << fixed << setprecision(10);
    in k;
    string s;
    cin>>k>>s;
    map<char,in> a;
    in n=s.size();
    rep(i,n) a[s[i]] ++;
    in ans=1ll;

    rep(i,k){
        in add=0ll;
        rep(j,26){
            char x='a'+j;
            add +=(n+1+i)-a[x];
        }
        add /=2ll;
        add %=MOD;
        ans *=add;
        ans %=MOD;
        a['a'] ++;
    }
    cout<<ans<<endl;
}/*
./problem.exe
*/