CF1455F String and Operations

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 $ .

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