human
Can you provide a Python code to find the number of ways in which we can select exactly K players such that the sum of their scores is the maximum possible given the following:
A cricket team consists of 11 players and some are good at batting, others are good at bowling and some of them are good at both batting and bowling. The batting coach wants to select exactly K players having maximum possible sum of scores. Given the batting score of each of the 11 players, find the number of ways in which we can select exactly K players such that the sum of their scores is the maximum possible. Two ways are different if there is a player who is selected in one of them is not in the other. See explanation of sample cases for more clarity.

Input
First line contains T, number of test cases ( 1 ≤ T ≤ 100 ). T cases follow, each having 2 lines. First line of each case contains scores of 11 players ( 1 ≤ score ≤ 100 ) and the second line contains K (1 ≤ K ≤ 11)

Output
For each test case, output the answer in a new line.

Example

Input:
2
1 2 3 4 5 6 7 8 9 10 11
3
2 5 1 2 4 1 6 5 2 2 1
6

Output:
1
6

Explanation:
Case 1 : Maximum possible sum of scores = 11 + 10 + 9 = 30 and can be achieved only by selecting the last 3 players. Only one possible way.
Case 2 : Maximum possible sum of scores = 6 + 5 + 5 + 4 + 2 + 2 = 24 and considering the players as p1 p2 p3 ... p11 in that order, the ones with maximum possible sum of scores is as follows
{p1, p2, p4, p5, p7, p8 }
{p10, p2, p4, p5, p7, p8 }
{p1, p2, p10, p5, p7, p8 }
{p9, p2, p4, p5, p7, p8 }
{p1, p2, p9, p5, p7, p8 }
{p10, p2, p9, p5, p7, p8 }
assistant
#Here is Python code to find the number of ways in which we can select exactly K players such that the sum of their scores is the maximum possible.

t=int(raw_input())
for i in range(t):
    
    c=raw_input()
    k=int(raw_input())
    c=c.split()
    for char in range(len(c)):
        c[char]=int(c[char])
    c=sorted(c)
    maximum_score=sum(c[-k:])
    no_ways=0
    def combinations(iterable, r):
        # combinations('ABCD', 2) --> AB AC AD BC BD CD
        # combinations(range(4), 3) --> 012 013 023 123
        pool = tuple(iterable)
        n = len(pool)
        if r > n:
            return
        indices = range(r)
        yield tuple(pool[i] for i in indices)
        while True:
            for i in range(r)[::-1]:
                if indices[i] != i + n - r:
                    break
            else:
                return
            indices[i] += 1
            for j in range(i+1, r):
                indices[j] = indices[j-1] + 1
            yield tuple(pool[i] for i in indices)
    cp=combinations([0,1,2,3,4,5,6,7,8,9,10],k)
    
    for combo in cp:
        sum1=0
        for d in combo:
            sum1+=c[d]
        if sum1==maximum_score:
            no_ways+=1
            
    print no_ways