Problem3255--Sereja and Intervals

3255: Sereja and Intervals

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Time Limit : 2.000 sec  Memory Limit : 256 MiB

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Description

time limit per test
1 second
memory limit per test
256 megabytes
input
standard input
output
standard output

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.

Input

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.

Output

In a single line print the answer modulo 1000000007 (109+7).

Examples
Input
1 1 1
Output
1
Input
3 5 1
Output
240
Input
2 3 3
Output
6
Note

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]}.

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