From 2011 facebook is organizing a Facebook hacker cup every year around feb, visit Facebook hacker cup homepage for more details

This question is the first question(Carried 20 marks out of 100) for the Round 1 of 2013 hacker cup. only top 500 contestants will be moved to Round 2.

## Problem Statement

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**.