You are given a string s and an integer k.

Define a function distance(s1, s2) between two strings s1 and s2 of the same length n as:

• The sum of the minimum distance between s1[i] and s2[i] when the characters from 'a' to 'z' are placed in a cyclic order, for all i in the range [0, n - 1].

For example, distance("ab", "cd") == 4, and distance("a", "z") == 1.

You can change any letter of s to any other lowercase English letter, any number of times.

Return a string denoting the lexicographically smallest string t you can get after some changes, such that distance(s, t) <= k.

 

Example 1:

Example 2:

Example 3:

 

Constraints:

• 1 <= s.length <= 100
• 0 <= k <= 2000
• s consists only of lowercase English letters.