A9185 | Sereja and Intervals

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 $1000000007$ $(10^{9}+7)$ .