Sereja and Intervals

有 $n$ 个区间，你需要为每个区间分配左右端点，端点属于 $[1,m]\cap \mathbb{N}$。你需要保证区间两两互不包含且至少存在一个区间的左端点等于 $x$，输出方案数对 $10^9+7$ 取模的结果，区间有标号。$nm\leqslant 10^5$，$1\leqslant x\leqslant m$。

Sereja is interested in intervals of numbers, so he has prepared a problem about intervals for you. An interval of numbers is a pair of integers $ [l,r] $ $ (1<=l<=r<=m) $ . Interval $ [l_{1},r_{1}] $ belongs to interval $ [l_{2},r_{2}] $ if the following condition is met: $ l_{2}<=l_{1}<=r_{1}<=r_{2} $ . Sereja wants to write out a sequence of $ n $ intervals $ [l_{1},r_{1}] $ , $ [l_{2},r_{2}] $ , $ ... $ , $ [l_{n},r_{n}] $ on a piece of paper. At that, no interval in the sequence can belong to some other interval of the sequence. Also, Sereja loves number $ x $ very much and he wants some (at least one) interval in the sequence to have $ l_{i}=x $ . Sereja wonders, how many distinct ways to write such intervals are there? Help Sereja and find the required number of ways modulo $ 1000000007 $ $ (10^{9}+7) $ . Two ways are considered distinct if there is such $ j $ $ (1<=j<=n) $ , that the $ j $ -th intervals in two corresponding sequences are not equal.

The first line contains integers $ n $ , $ m $ , $ x $ $ (1<=n·m<=100000,1<=x<=m) $ — the number of segments in the sequence, the constraints on the numbers in segments and Sereja's favourite number.

In a single line print the answer modulo $ 1000000007 $ $ (10^{9}+7) $ .

1 1 1

1

3 5 1

240

2 3 3

6

In third example next sequences will be correct: $ {[1,1],[3,3]} $ , $ {[1,2],[3,3]} $ , $ {[2,2],[3,3]} $ , $ {[3,3],[1,1]} $ , $ {[3,3],[2,2]} $ , $ {[3,3],[1,2]} $ .