Problem Statement

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.

Constraints

• 1 \leq N \leq 10^6
• 0 \leq A \leq N-1
• 0 \leq B \leq N-1

Sample Input 1

3 0 0

Sample Output 1

1

The only good permutation is (0,2,1).

Sample Input 2

12 2 3

Sample Output 2

5390

Sample Input 3

10000 9875 5431

Sample Output 3

135608808