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!
Sample Input
2 1
3 -1
4 1
Sample Output
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有獎月賽-2011年03月