High-Rise Buildings

A neighborhood has N buildings in a row. All building heights are distinct, and each height is an integer from 1 to N.

When the row is viewed from one side, a building is visible only if it is taller than every building before it from that side. On the way to school, Sanggeun counted L visible buildings from the left. On the way home, he counted R visible buildings from the right.

Given N, L, and R, count how many height orders satisfy both visibility counts.

For instance, when N = 5, L = 3, and R = 2, 1 3 5 2 4 is one valid order.

The first line contains three space-separated integers N, L, and R: the number of buildings, the number visible from the left, and the number visible from the right.

Print the number of valid building orders modulo 1,000,000,007.

• 1 <= N <= 100
• 1 <= L, R <= N