public final class Solution

                    

2842 - Count K-Subsequences of a String With Maximum Beauty.

Hard

You are given a string s and an integer k.

A k-subsequence is a subsequence of s, having length k, and all its characters are unique , i.e., every character occurs once.

Let f(c) denote the number of times the character c occurs in s.

The beauty of a k-subsequence is the sum of f(c) for every character c in the k-subsequence.

For example, consider s = "abbbdd" and k = 2:

• f('a') = 1, f('b') = 3, f('d') = 2

• Some k-subsequences of s are:

Return an integer denoting the number of k-subsequences whose beauty is the maximum among all k-subsequences. Since the answer may be too large, return it modulo <code>10⁹ + 7</code>.

A subsequence of a string is a new string formed from the original string by deleting some (possibly none) of the characters without disturbing the relative positions of the remaining characters.

Notes

• f(c) is the number of times a character c occurs in s, not a k-subsequence.

• Two k-subsequences are considered different if one is formed by an index that is not present in the other. So, two k-subsequences may form the same string.

Example 1:

Input: s = "bcca", k = 2

Output: 4

Explanation: From s we have f('a') = 1, f('b') = 1, and f('c') = 2. The k-subsequences of s are:

**<ins>bc</ins>**ca having a beauty of f('b') + f('c') = 3

**<ins>b</ins>**c<ins> c </ins>a having a beauty of f('b') + f('c') = 3

<ins>b</ins>cc<ins>a</ins> having a beauty of f('b') + f('a') = 2

b**<ins>c</ins>**c<ins> a </ins> having a beauty of f('c') + f('a') = 3

bc**<ins>ca</ins>** having a beauty of f('c') + f('a') = 3

There are 4 k-subsequences that have the maximum beauty, 3. Hence, the answer is 4.

Example 2:

Input: s = "abbcd", k = 4

Output: 2

Explanation: From s we have f('a') = 1, f('b') = 2, f('c') = 1, and f('d') = 1. The k-subsequences of s are:

<ins> **ab** </ins>b**<ins>cd</ins>** having a beauty of f('a') + f('b') + f('c') + f('d') = 5<ins> **a** </ins>b<ins> **bcd** </ins> having a beauty of f('a') + f('b') + f('c') + f('d') = 5

There are 2 k-subsequences that have the maximum beauty, 5. Hence, the answer is 2.

Constraints:

• <code>1 <= s.length <= 2 * 10⁵</code>

• 1 <= k <= s.length

• s consists only of lowercase English letters.