Back From Summer '19 P3: ASDFGHJKL

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Points: 10 (partial)
Time limit: 1.0s
Memory limit: 128M

Problem type

Jonathan is given a string S containing solely lowercase English letters. He is asked to perform the two following operations in order exactly once:

  • Remove a substring of length up to L (inclusive) from the string.
  • Remove up to K (inclusive) characters from the remaining string.

Let c_a be the number of a's in the resultant string, c_b be the number of b's, etc. Jonathan's goal is to minimize c_a^2 + c_b^2 + \dots + c_z^2 after performing the two operations. What is the minimum possible value?

Python users are recommended to use PyPy over CPython. There is a significant performance increase.

Input Specification

The first line will contain the string S (1 \le |S| \le 10^5). S will only contain lowercase English letters.

The second line will contain two integers, L, K (0 \le L, K \le |S|).

Output Specification

Output the minimum possible value of c_a^2 + c_b^2 + \dots + c_z^2 for Jonathan.


Subtask 1 [30%]

L = 0

Subtask 2 [70%]

No additional constraints.

Sample Input 1

0 5

Sample Output 1


Sample Input 2

3 2

Sample Output 2



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