Skyscrapers#1535
The skyline of the city has buildings in a straight line; each building has a distinct height from to . A building is visible from the left if there is no taller building to its left. Similarly, a building is visible from the right if there is no taller building to its right. For example, if the buildings are in the order \{1, 3, 5, 2, 4\}, three buildings () are visible from the left, and two () are visible from the right.
You are given the total number of buildings , the number of buildings visible from the left, and the number of buildings visible from the right. Find the number of permutations of the buildings that satisfy these conditions.
Each line is a separate test case and contains values n~(1 \le n \le 100), , and r~(1 \le l, r \le n).
For each test case, print in a separate line the number of permutations of the buildings that satisfy the given conditions. Print the result modulo 10^9 + 7.
Example 1