Problem Description

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 Format

Input is given from Standard Input in the following format:

\( N \) \( A \) \( B \)

Output Format

Print the number of good permutations modulo \( 10^9+7 \).

Sample Input and Output

Sample Input #1

3 0 0

Sample Output #1

1

Sample Input #2

12 2 3

Sample Output #2

5390

Sample Input #3

10000 9875 5431

Sample Output #3

135608808

Notes/Hints

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 \( (0,2,1) \).

见题面 Input 部分

见题面 Output 部分