AT_jag2018summer_day2_k Short LIS

[problemUrl]: https://atcoder.jp/contests/jag2018summer-day2/tasks/jag2018summer_day2_k You are given three integers $ N $, $ A $, and $ B $. Let $ P=(P_0,P_1,...,P_{N-1}) $ be a permutation of $ (0,1,...,N-1) $. $ P $ is said **good** if and only if it satisfies all of the following conditions: - The length of a longest increasing subsequence of $ P $ is at most $ 2 $. - $ P_A\ =\ B $ Count the number of good permutations modulo $ 10^9+7 $.

Input is given from Standard Input in the following format: > $ N $ $ A $ $ B $

Print the number of good permutations modulo $ 10^9+7 $.

### Constraints - $ 1\ \leq\ N\ \leq\ 10^6 $ - $ 0\ \leq\ A\ \leq\ N-1 $ - $ 0\ \leq\ B\ \leq\ N-1 $ ### Sample Explanation 1 The only good permutation is $ (0,2,1) $.