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: Accepted)

arr = gets.chomp.chars
K = gets.chomp.to_i
N = arr.size
count = K

class String
    # a..z → 0..25
    def assign_integer
        ord - 'a'.ord
    end

    # 引数分だけアルファベットを進める
    def change_char(num)
        ((assign_integer + num) % 26).assign_alphabet
    end
end

class Integer
    # 0..25 → a..z
    def assign_alphabet
        (self + 'a'.ord).chr
    end
end

(0..K - 1).each do |i|
    if count == 0
        break
    elsif i == N - 1
        arr[i] = arr[i].change_char(count)
        break
    elsif arr[i] == 'a'
        next
    elsif arr[i].assign_integer + count > 25
        int = arr[i].assign_integer
        arr[i] = arr[i].change_char(26 - int)
        count = count - 26 + int
    end
end

puts arr.join('')