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 Python (3.8.2) (judge verdict: Runtime Error)

K = int(input())
S = len(input())

mod = int(1e9 + 7)

def memorize(f):
    dic = {}
    def main(*args):
        if args not in dic:
            dic[args] = f(*args)
        return dic[args]
    return main
    
# @memorize
def fpow(x, n):
    ret = 1
    tmp = x
    while n:
        if n & 1:
            ret = ret * tmp % mod
        tmp = tmp * tmp % mod
        n >>= 1
    return ret
    
# @memorize
def inv(x):
    return fpow(x, mod - 2)
    
@memorize
def fact(x):
    if x == 0:
        return 1
    return fact(x - 1) * x % mod
    
# @memorize
def C(n, m):
    return fact(n) * inv(fact(m)) * inv(fact(n - m)) % mod
    
ret = 0
for i in range(S, S + K + 1):
    ret = (ret + C(i - 1, i - S) * fpow(25, i - S) * fpow(26, S + K - i)) % mod
print(ret)