# #P367E. Sereja and Intervals

ID: 5472 Type: RemoteJudge 1000ms 256MiB 尝试: 2 已通过: 2 难度: 10 上传者: 标签>combinatoricsdp*2700

# Sereja and Intervals

## Description

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).

## 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).

## Samples

``````1 1 1

``````
``````1

``````
``````3 5 1

``````
``````240

``````
``````2 3 3

``````
``````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]}.