hackercupai/hackercup huggingface dataset:
John is playing a game with his friends. The game's rules are as follows:
There is deck of **N** cards from which each person is dealt a hand of **K**
cards. Each card has an integer value representing its strength. A hand's
strength is determined by the value of the highest card in the hand. The
person with the strongest hand wins the round. Bets are placed before each
player reveals the strength of their hand.

John needs your help to decide when to bet. He decides he wants to bet when
the strength of his hand is higher than the average hand strength. Hence John
wants to calculate the average strength of ALL possible sets of hands. John is
very good at division, but he needs your help in calculating the sum of the
strengths of all possible hands.

## Problem

You are given an array **a** with **N ≤ 10,000** different integer numbers and
a number, **K**, where **1 ≤ K ≤ N**. For all possible subsets of **a** of
size **K** find the sum of their maximal elements modulo **1,000,000,007**.

## Input

The first line contains the number of test cases **T**, where ** 1 ≤ T ≤ 25 **

Each case begins with a line containing integers **N** and **K**. The next
line contains **N** space-separated numbers **0 ≤ a [i] ≤ 2,000,000,000**,
which describe the array **a**.

## Output

For test case **i**, numbered from **1** to **T**, output "Case #i: ",
followed by a single integer, the sum of maximal elements for all subsets of
size **K** modulo 1,000,000,007.

## Example

For **a = [3, 6, 2, 8]** and **N = 4** and **K = 3**, the maximal numbers
among all triples are **6, 8, 8, 8** and the sum is **30**.