Kangaroo

A garden is one row of $N$ cells numbered 1 to $N$. Every cell holds a plant at the start.

A kangaroo lands on cell $c_s$ and eats the plant there. After that it jumps from cell to cell, eats the plant in every cell it lands on, visits all $N$ cells exactly once, and stops on cell $c_f$. The starting cell and the last cell count as visited, so the kangaroo makes exactly $N-1$ jumps.

To avoid being caught, the kangaroo changes the direction of its next jump after every jump. If it jumped from cell $prev$ to cell $current$ and then jumps from cell $current$ to cell $next$, both conditions below hold.

• If $prev < current$, then $next < current$.
• If $current < prev$, then $current < next$.

Given the number of cells $N$, the starting cell $c_s$, and the last cell $c_f$, count the distinct routes the kangaroo can take.

The first line contains the positive integers $N$, $c_s$, $c_f$, separated by spaces.

• $2 \le N \le 2000$
• $1 \le c_s \le N$
• $1 \le c_f \le N$
• $c_s \ne c_f$
• A route is determined by the order in which the cells are visited.
• Every input has at least one route that follows the rules.
• The kangaroo may make its first jump from cell $c_s$ in either direction.

Print the number of distinct routes that follow the rules, modulo $1000000007$ ($10^9 + 7$), on one line.

In the first example the kangaroo starts on cell 2 and stops on cell 3. Two routes follow the rules: 2 → 1 → 4 → 3 and 2 → 4 → 1 → 3.