A10195. Bear and String Distance

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, , and .

Also, the distance between two nice strings is defined as the sum of distances of corresponding letters. For example, , and .

Limak gives you a nice string $s$ and an integer $k$ . He challenges you to find any nice string $s'$ that . 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.

The first line contains two integers $n$ and $k$ ( $1<=n<=10^{5}$ , $0<=k<=10^{6}$ ).

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

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

Otherwise, print any nice string $s'$ that .