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 $P$.

Constraints

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

Input

Input is given from Standard Input in the following format:

$N$ $pos$ $val$

Output

Print the answer.

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