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;
 
#define IOS ios::sync_with_stdio(0); cin.tie(0); cout.tie(0);
#define endl "\n"
#define int long long

const int N = 2e6 + 5;
const int MOD = 1e9 + 7;

int pow(int a, int b, int m)
{
	int ans=1;
	while(b)
	{
		if(b&1)
			ans=(ans*a)%m;
		b/=2;
		a=(a*a)%m;
	}
	return ans;
}

int fact[N], invfact[N];

int modinv(int k)
{
	return pow(k, MOD-2, MOD);
}

void precompute()
{
	fact[0]=fact[1]=1;
	for(int i=2;i<N;i++)
	{
		fact[i]=fact[i-1]*i;
		fact[i]%=MOD;
	}
	invfact[N-1]=modinv(fact[N-1]);
	for(int i=N-2;i>=0;i--)
	{
		invfact[i]=invfact[i+1]*(i+1);
		invfact[i]%=MOD;
	}
}

int nCr(int x, int y)
{
	if(y>x)
		return 0;
	int num=fact[x];
	num*=invfact[y];
	num%=MOD;
	num*=invfact[x-y];
	num%=MOD;
	return num;
}

int n, k;
string s;

int32_t main()
{
	IOS;
	precompute();
	cin >> k >> s;
	n = s.size();
	int ans = 0;
	for(int len = n; len <= n + k; len++)
	{
		int cur = pow(26, n + k - len, MOD) * pow(25, len - n, MOD);
		cur %= MOD;
		cur *= nCr(len - 1, n - 1);
		cur %= MOD;
		ans += cur;
		ans %= MOD;
	}
	cout << ans;
	return 0;
}