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.times do
    case char
    when 'a'..'y'
      char = char.next
    when 'z'
      char = 'a'
    end
  end

  char
end

def solve(word, n, answer)
  puts "solve: #{word}, #{n}"
  # a に変換するために消費する N (z.ord = 122)
  required_n = 122 - word[0].ord + 1

  if (n >= required_n && word.length > 1)
    solve(word[1..-1], n - required_n, answer + 'a')
  else
    # 現在の残り N で a に変換できるものを探す
    tmp_word = word
    tmp_word.each_char.with_index do |char, i|
      required_n = 122 - char.ord + 1
      if required_n != 0 && n >= required_n
        word[i] = 'a'
        n -= required_n
      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 answer + word
  end
end

puts solve(WORD, N, "")