You are given a string s and an integer k.

A $k$ subsequence is a subsequence of s of length k that contains k distinct characters.

Let $f(c)$ denote the frequency of character $c$ in s. The beauty of a $k$ subsequence is the sum of $f(c)$ for all characters $c$ present in the subsequence.

Return the total number of $k$ subsequences that achieve the maximum possible beauty. Since the result may be large, return it modulo $10^9 + 7$.

If no such subsequence exists, return $0$.

Note:
Two subsequences are considered different if they are chosen from different sets of indices in s.

Constraints:

• $1 \leq$ s.length $\leq 2 \cdot 10^5$

• $1 \leq$ k $\leq$ s.length

• s consists only of lowercase English letters.

Now, let’s take a moment to make sure you’ve correctly understood the problem. The quiz below helps you check if you’re solving the correct problem:

We have a game for you to play. Rearrange the logical building blocks to develop a clearer understanding of how to solve this problem.

Implement your solution in the following coding playground.