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Given an integer. Find how many structurally unique binary search trees are there that stores the values from 1 to that integer (inclusive). 

Example 1:

Input:
N = 2
Output: 2
Explanation:for N = 2, there are 2 unique
BSTs
     1               2  
      \            /
       2         1

Example 2:

Input:
N = 3
Output: 5
Explanation: for N = 3, there are 5
possible BSTs
  1           3     3       2     1
    \        /     /      /  \     \
     3      2     1      1    3     2
    /      /       \                 \
   2      1         2                 3

 

Your Task:
You don't need to read input or print anything. Your task is to complete the function numTrees() which takes the integer N as input and returns the total number of Binary Search Trees possible with keys [1.....N] inclusive. Since the answer can be very large, return the answer modulo 1000000007.

Expected Time Complexity: O(N2).
Expected Auxiliary Space: O(N).

Constraints:
1<=N<=1000

** For More Input/Output Examples Use 'Expected Output' option **

Author: dhruvi


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