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

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

Input

Input is given from Standard Input in the following format:

$N$ $A$ $B$

Output

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

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