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 PyPy3 (7.3.0) (judge verdict: Runtime Error)

n = 10**6
mod = 10 ** 9 + 7
fact = [1]*(n+1)
rfact = [1]*(n+1)
r = 1
for i in range(1, n+1):
  fact[i] = r = r * i % mod
rfact[n] = r = pow(fact[n], mod-2, mod)
for i in range(n, 0, -1):
  rfact[i-1] = r = r * i % mod

# nPk (mod MOD) を求める
def perm(n, k):
  return fact[n] * rfact[n-k] % mod

# nCk (mod MOD) を求める
def comb(n, k):
  return fact[n] * rfact[k] * rfact[n-k] % mod

k = int(input())
s = input()

len_s = len(s)
ans = 0
for i in range(len_s,k+len_s+1):
    ans += (comb(i-1,len_s-1) * pow(25,i-len_s,mod) * pow(26,k+len_s-i,mod)) % mod
    ans %= mod
print(ans)