Phoenix Locks the Door

Where is Phoenix's house? People assume Phoenix lives at POSTECH, but he actually lives in the Phoenix village high in the sky. Outsiders can hardly reach the village, and since phoenixes are born righteous, they often forget to lock their doors.

Phoenix is no exception. Every day he travels between POSTECH and the village without locking his door. One day, while Phoenix was away from home, Mr. K, a famous thief from POSTECH, installed a lock on Phoenix's house! The lock is made of $N$ dials connected together, and each dial has the uppercase letters A through Z written in order.

To open the lock, Phoenix can pick one dial and turn it $1$ step. The letter shown on the chosen dial changes from A to B, B to C, ..., and Z to A. Dials cannot be turned in the opposite direction. Phoenix has learned that the password is the lexicographically smallest string he can display after performing exactly $K$ turns. Help Phoenix get his house back by finding the password.

The first line contains the length $N$ of the lock and the number of turns $K$, separated by a space. $(1 \le N \le 200\ 000; 0 \le K \le 1\ 000\ 000)$

The second line contains the string $S$ of length $N$ currently shown on the lock. $S$ consists only of uppercase letters.

Print the lexicographically smallest string that can be displayed by turning the dials exactly $K$ times.

For two strings $A$ and $B$ of the same length $N$, $A$ is lexicographically smaller than $B$ if there is an integer $i$ that satisfies the following conditions.

• $1 \le i \le N$
• $A_j = B_j$ for all $1 \le j < i$
• $A_i \ne B_i$, and $A_i$ comes before $B_i$ in alphabetical order.