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') = 2s are:\n\t"abbbdd" -> "ab" having a beauty of f('a') + f('b') = 4"abbbdd" -> "ad" having a beauty of f('a') + f('d') = 3"abbbdd" -> "bd" having a beauty of f('b') + f('d') = 5Return 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 109 + 7.
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.
\n\nNotes
\n\nf(c) is the number of times a character c occurs in s, not a k-subsequence.\n
Example 1:
\n\n\nInput: s = "bcca", k = 2\nOutput: 4\nExplanation: From s we have f('a') = 1, f('b') = 1, and f('c') = 2.\nThe k-subsequences of s are: \nbcca having a beauty of f('b') + f('c') = 3 \nbcca having a beauty of f('b') + f('c') = 3 \nbcca having a beauty of f('b') + f('a') = 2 \nbcca having a beauty of f('c') + f('a') = 3\nbcca having a beauty of f('c') + f('a') = 3 \nThere are 4 k-subsequences that have the maximum beauty, 3. \nHence, the answer is 4. \n\n\nExample 2:
\n\n\nInput: s = "abbcd", k = 4\nOutput: 2\nExplanation: From s we have f('a') = 1, f('b') = 2, f('c') = 1, and f('d') = 1. \nThe k-subsequences of s are: \nabbcd having a beauty of f('a') + f('b') + f('c') + f('d') = 5\nabbcd having a beauty of f('a') + f('b') + f('c') + f('d') = 5 \nThere are 2 k-subsequences that have the maximum beauty, 5. \nHence, the answer is 2. \n\n\n\n
Constraints:
\n\n1 <= s.length <= 2 * 1051 <= k <= s.lengths consists only of lowercase English letters.k characters such that the sum of their frequencies is maximum.",
"An obvious case to eliminate is if k is greater than the number of distinct characters in s, then the answer is 0.",
"We are now interested in the top frequencies among the characters. Using a map data structure, let cnt[x] denote the number of characters that have a frequency of x.",
"Starting from the maximum value x in cnt. Let i = min(k, cnt[x]) we add to our result cnt[x]Ci * xi representing the number of ways to select i characters from all characters with frequency x, multiplied by the number of ways to choose each individual character. Subtract i from k and continue downwards to the next maximum value.",
"Powers, combinations, and additions should be done modulo 109 + 7."
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