Skyscrapers

The skyline of the city has $n$ buildings all in a straight line; each building has a distinct height between $1$ and $n$, inclusive. The building at index $i$ is considered visible from the left if there is no building with a smaller index that is taller. Similarly, a building is visible from the right if there is no taller building with a higher index. For example, if the buildings in order are $\{1,3,5,2,4\}$, then three buildings are visible from the left $(1,3,5)$, but only two are visible from the right ($4$ and $5$).

You will be given the total number of buildings $n,l$ buildings visible from the left, and $r$ buildings visible from the right. Find the number of permutations of the buildings that are consistent with these values.

Input

Each line is a separate test case that contains the values of $n(1\le n\le 100)$, $l$ and $r(1\le l,r\le n)$.

Output

For each test case print in a separate line the number of permutations of the buildings that are consistent with the given values. The results must be printed modulo $10^9+7$.

Examples