HC12 - Card Game

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.

Sample

Input:
5
4 3
3 6 2 8
5 2
10 20 30 40 50
6 4
0 1 2 3 5 8
2 2
1069 1122
10 5
10386 10257 10432 10087 10381 10035 10167 10206 10347 10088

Output:
Case #1: 30
Case #2: 400
Case #3: 103
Case #4: 1122
Case #5: 2621483

Added by:abdelkarim
Date:2013-02-02
Time limit:1s
Source limit:5000B
Memory limit:1536MB
Cluster: Cube (Intel G860)
Languages:All except: ASM64
Resource:Facebook Hacker Cup 2013 Round 1

hide comments
2013-02-06 17:42:07 Ehor Nechiporenko
Yep, @Franky, but I haven't tried one more optimization. Not the whole array should be sorted ;-)
2013-02-06 17:42:07 Francky
It seems it could be hard to do less than 0.05s ; only r**d and s**t cost me 0.04s, ... I'll try a python shot to see if feasible.
Edit : It seems really hard to optimize a python solution to get AC, I think time limit should be increased to give a chance to python users, this will not allow 'bad' solutions in fast language to get AC. Please consider this.
@ Ehor : I'll can't follow you on this way, it's yet one of the first time I use a c++ container, ... and sorting is not my cup of tea, I let std do that. But why not try this in Python if time limit is given better. Interesting. ;-)

Edit(by abdelkarim) : now python solutions can get AC ;-) .
--ans(Francky)--> Many thanks for this little help. This give a good challenge for fastest solvers. ;-)

Last edit: 2013-02-06 18:26:27
2013-02-06 17:42:07 Ehor Nechiporenko
Nice problem, optimized to make source the fastest)
2013-02-06 17:42:07 Problem Solver
Really cool problem! Thank you.
2013-02-06 17:42:07 (Tjandra Satria Gunawan)(曾毅昆)
Nice problem (and nice source limit :-P), please change the cluster to pyramid, I want to know my program running time more accurately..
---ps---
cluster has been changed to pyramid ;-) .
EDIT(Tjandra): Thanks :-D

Last edit: 2013-02-05 22:18:09
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