| 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**. | |