Statement

Since spring is coming and thus the tree planting season is about to start as well, Alice and Bob decided to start planning their future adventures. One day, Bob came with the idea that they could spend their time together planting trees in the magic forest. Since this is a magic forest, the trees they can plant are in fact binary trees! However, they are not just any kind of binary tree, but rooted binary trees with root at node 1 and with the property that there are more nodes on the left side of the tree than on the right side of the tree. This spring they decided that the trees they are going to plant are of size N. Since they want to spend as much time as possible in the magic forest, let them know how many distinct binary trees with N nodes exist such that there are more nodes on the left side of the tree than on the right side of the tree. Since the answer is big, print it modulo 10^9 + 7...