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Problem 2015 Vote

## Problem Description

Here are n Candidates in one election. Every Candidate could vote any one (of course himself/herself). In this election, the one who gets more than half of n become the winner! However, sometimes no winner could be determined (No one gets more than half of n votes)!

Now you are given the number of Candidates and the final winner m, here if m is equal to -1, then it means that no one wins, otherwise m is the index of the Candidate. (The index of Candidates is 0, 1, 2, … n – 1 respectively) Abcdxyzk wants to know the number of possible ways of the final result if the winner if m. (m = -1 for no winner of course) However, the answer maybe large, so abcdxyzk just want the remainder of the answer after divided by 1000000007.

## Input

There are several test cases.

For each case, only two integers n and m in a single line indicates n Candidates and the final winner m. (1 <= n <= 100, -1 <= m < n)

## Output

For each test case, output the number of possible ways of the final election!

2 1 3 -1 4 1

1 1 4

## Hint

In case 1, only one possible ways of the final result because both 0 and 1 vote to 1.

In case 2, only one possible ways of the final result because all of 0, 1, and 2 get one vote.

In case 3, there are 4 possible ways of final result:

(1) 0: 1 (vote(s)) 1: 3 (vote(s)) 2: 0 (vote(s)) 3: 0 (vote(s))

(2) 0: 0 (vote(s)) 1: 3 (vote(s)) 2: 1 (vote(s)) 3: 0 (vote(s))

(3) 0: 0 (vote(s)) 1: 3 (vote(s)) 2: 0 (vote(s)) 3: 1 (vote(s))

(4) 0: 0 (vote(s)) 1: 4 (vote(s)) 2: 0 (vote(s)) 3: 0 (vote(s))

## Source

FOJ有奖月赛-2011年03月

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