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 Ruby (2.7.1) (judge verdict: Accepted)

M=10**9+7
def extended_gcd(a, b)
  last_remainder, remainder = a.abs, b.abs
  x, last_x, y, last_y = 0, 1, 1, 0
  while remainder != 0
    last_remainder, (quotient, remainder) = remainder, last_remainder.divmod(remainder)
    x, last_x = last_x - quotient*x, x
    y, last_y = last_y - quotient*y, y
  end
  return last_remainder, last_x * (a < 0 ? -1 : 1)
end

def invmod(e)
  g, x = extended_gcd(e, M)
  x % M
end

k=gets.to_i
n=gets.chomp.size
z=zinv=invmod(26)
q=invmod((2..k).reduce(1){|s,e| s*e%M })
qs=[]
k.downto(0){|i|
  qs[i]=q
  q=q*i%M
  z=z*26%M
}
puts (0..k).reduce(0){|s,i|
  s=(s+z*qs[i])%M
  z=z*25*(n+i)*zinv%M
  s
}