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)

import bisect, collections, copy, heapq, itertools, math, numpy, string
import sys
from bisect import bisect_left, bisect_right, insort
from collections import deque
def S(): return sys.stdin.readline().rstrip()
def I(): return int(sys.stdin.readline().rstrip())
def MI(): return map(int, sys.stdin.readline().rstrip().split())
def MS(): return map(str, sys.stdin.readline().rstrip().split())
def LI(): return list(map(int, sys.stdin.readline().rstrip().split()))
def LS(): return list(sys.stdin.readline().rstrip().split())
# N = I()
# A = [LI() for _ in range(N)]


k = I()
s = S()
p = 10**9 + 7
ans = pow(26,len(s) + k,p)
a = 0
aa = list(itertools.combinations_with_replacement(range(k),len(s)))
for i in range(len(aa)):
    ans -= pow(26,aa[i][0],p)
    for j in range(1,len(s)):
        ans -= pow(26,aa[i][i]-aa[i][i-1],p)
    ans -= pow(26,len(s) + k - aa[i][-1],p)
print(ans%p)