Problem:
Score : 400 points

Problem Statement

Mr. Takahashi has a string s consisting of lowercase English letters.
He repeats the following operation on s exactly K times.

Choose an arbitrary letter on s and change that letter to the next alphabet. Note that the next letter of z is a.

For example, if you perform an operation for the second letter on aaz, aaz becomes abz.
If you then perform an operation for the third letter on abz, abz becomes aba.

Mr. Takahashi wants to have the lexicographically smallest string after performing exactly K operations on s.
Find the such string.

Constraints

1≤|s|≤10^5

All letters in s are lowercase English letters.

1≤K≤10^9

Input

The input is given from Standard Input in the following format:

s
K

Output

Print the lexicographically smallest string after performing exactly K operations on s.

Sample Input 1

xyz
4

Sample Output 1

aya

For example, you can perform the following operations: xyz, yyz, zyz, ayz, aya.

Sample Input 2

a
25

Sample Output 2

z

You have to perform exactly K operations.

Sample Input 3

codefestival
100

Sample Output 3

aaaafeaaivap

Solution in Ruby (2.3.3) (judge verdict: Wrong Answer)

WORD = gets.chomp
N = gets.chomp.to_i

def next_char(char, n = 1)
  (n % 26).times do
    case char
    when 'a'..'y'
      char = char.next
    when 'z'
      char = 'a'
    end
  end

  char
end

def solve(word, n)
  tmp_word = word
  tmp_word.each_char.with_index do |char, i|
    # a に変換するために消費する N (z.ord = 122)
    required_n = 122 - tmp_word[i].ord + 1

    if n >= required_n
      word[i] = 'a'
      n -= required_n
    else
      next
    end
  end

  # それでも余れば最後の文字に足す
  if (n >= 0)
    word[-1] = next_char(word[-1], n)
  end

  return word
end

puts solve(WORD, N)