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.