Limak is a little polar bear. He likes nice strings — strings of length n, consisting of lowercase English letters only.

The distance between two letters is defined as the difference between their positions in the alphabet. For example, $\text{[math]}$ , and $\text{[math]}$ .

Also, the distance between two nice strings is defined as the sum of distances of corresponding letters. For example, $\text{[math]}$ , and $\text{[math]}$ .

Limak gives you a nice string s and an integer k. He challenges you to find any nice string s' that $\text{[math]}$ . Find any s' satisfying the given conditions, or print "-1" if it's impossible to do so.

As input/output can reach huge size it is recommended to use fast input/output methods: for example, prefer to use gets/scanf/printf instead of getline/cin/cout in C++, prefer to use BufferedReader/PrintWriter instead of Scanner/System.out in Java.

Input

The first line contains two integers n and k (1 ≤ n ≤ 10⁵, 0 ≤ k ≤ 10⁶).

The second line contains a string s of length n, consisting of lowercase English letters.

Output

If there is no string satisfying the given conditions then print "-1" (without the quotes).

Otherwise, print any nice string s' that $\text{[math]}$ .

Bear and String Distance

Examples