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: Time Limit Exceeded)

import math
k = int(input())
s = input()

ss = len(s)

mod = 10**9 + 7

m25 = []
m26 = []
a = 1
b = 1

for i in range(k+1):
    m25.append(a)
    a *= 25
    a %= mod

for i in range(k+1):
    m26.append(b)
    b *= 26
    b %= mod

samu = 0
for i in range(k+1):
    sm = math.factorial(ss+k-i-1) // (math.factorial(ss-1) * math.factorial(k-i))
    sm %= mod
    sm *= m25[k-i]
    sm *= m26[i]
    sm %= mod
    samu += sm

samu %= mod
print(samu)