Lexicographically Smallest String with Bounded Similarity

You are given an integer n, two integers l and r, and a lowercase letter string s of length n. The similarity between two strings a and b of length n is defined as

where \([a_i=b_i]\) is 1 if \(a_i=b_i\) and 0 otherwise.

Your task is to construct a lowercase letter string t of length n such that the similarity between t and the given string s is between l and r (inclusive). Among all such strings t, you must output the lexicographically smallest one.

Note: The letters are chosen from the set \(\{a, b, \ldots, z\}\). The lexicographical order is the usual dictionary order.

inputFormat

The first line contains three integers n, l, and r.

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

outputFormat

Output the lexicographically smallest string t of length n that satisfies
$$l\le \sum_{i=1}^{n}[t_i=s_i]\le r.$$

sample

2 1 1
cb

ab