You are given a string $s$ consisting of $n$ characters. These characters are among the first $k$ lowercase letters of the Latin alphabet. You have to perform $n$ operations with the string.

During the $i$-th operation, you take the character that initially occupied the $i$-th position, and perform one of the following actions with it:

• swap it with the previous character in the string (if it exists). This operation is represented as L;
• swap it with the next character in the string (if it exists). This operation is represented as R;
• cyclically change it to the previous character in the alphabet (b becomes a, c becomes b, and so on; a becomes the $k$-th letter of the Latin alphabet). This operation is represented as D;
• cyclically change it to the next character in the alphabet (a becomes b, b becomes c, and so on; the $k$-th letter of the Latin alphabet becomes a). This operation is represented as U;
• do nothing. This operation is represented as 0.

For example, suppose the initial string is test, $k = 20$, and the sequence of operations is URLD. Then the string is transformed as follows:

1. the first operation is U, so we change the underlined letter in test to the next one in the first $20$ Latin letters, which is a. The string is now aest;
2. the second operation is R, so we swap the underlined letter with the next one in the string aest. The string is now aset;
3. the third operation is L, so we swap the underlined letter with the previous one in the string aset (note that this is now the $2$-nd character of the string, but it was initially the $3$-rd one, so the $3$-rd operation is performed to it). The resulting string is saet;
4. the fourth operation is D, so we change the underlined letter in saet to the previous one in the first $20$ Latin letters, which is s. The string is now saes.

The result of performing the sequence of operations is saes.

Given the string $s$ and the value of $k$, find the lexicographically smallest string that can be obtained after applying a sequence of operations to $s$.