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 $5$). \includegraphics{https://static.e-olymp.com/content/e9/e90fd5225e150fffd2802ef93cfb3f8da8c779d4.gif} 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. \InputFile Each line is a separate test case that contains the values of $n~(1 \le n \le 100)$, $l$ and $r~(1 \le l, r \le n)$. \OutputFile 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 $10^9 + 7$.