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 [l1,r1] belongs to interval [l2,r2] if the following condition is met: l2≤l1≤r1≤r2.
Sereja wants to write out a sequence of n intervals [l1,r1], [l2,r2], ..., [ln,rn] 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 li=x. Sereja wonders, how many distinct ways to write such intervals are there?
Help Sereja and find the required number of ways modulo 1000000007 (109+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 (109+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]}.