Next Letter

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.

Examples

Input

xyz 4

Output

aya

Input

a 25

Output

z

Input

codefestival 100

Output

aaaafeaaivap

inputFormat

Input

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

s K

outputFormat

Output

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

Examples

Input

xyz 4

Output

aya

Input

a 25

Output

z

Input

codefestival 100

Output

aaaafeaaivap

样例

codefestival
100

aaaafeaaivap