Problem Statement

Given N, pos, val, find the number of permutations $P=(P_1, P_2, \ldots, P_N)$ of $(1,2,\ldots,N)$ that satisfy all of the following conditions, modulo 10^9+7:

• LIS(P) + LDS(P) = N+1
• P_{pos} = val

Here, LIS(P) denotes the length of the longest increasing subsequence of P, and LDS(P) denotes the length of the longest decreasing subsequence of P.

Input

Input is given from Standard Input in the following format:
N pos val

Output

Print the answer.

Constraints

• $1 \le N \le 5\cdot 10^6$
• $1 \le pos, val \le N$
• All values in the input are integers.

Sample Input 1

3 2 2

Sample Output 1

2

The following permutations satisfy the conditions: (1, 2, 3), (3, 2, 1).

Sample Input 2

4 1 1

Sample Output 2

6

The following permutations satisfy the conditions: (1, 2, 3, 4), (1, 2, 4, 3), (1, 3, 2, 4), (1, 3, 4, 2), (1, 4, 2, 3), (1, 4, 3, 2).

Sample Input 3

5 2 5

Sample Output 3

11

Sample Input 4

2022 69 420

Sample Output 4

128873576

见题面 Input 部分

见题面 Output 部分