Software Developer

Goku has ‘N’ Dragon Balls. Each Dragon Ball is unique with the ith Dragon Ball having ‘i’ stars on it. For example, the first Dragon Ball has 1 star, the second Dragon Ball has 2 stars, and so on.

Goku gave a task to Gohan to arrange the ‘N’ Dragon Balls in a binary tree-like structure. While making the binary tree, he has to make sure that these conditions must be fulfilled:

The left subtree of any particular Dragon Ball ‘D’ will always contain Dragon Balls with the number of stars less than that of the Dragon Ball ‘D’.

The right subtree of any particular Dragon Ball ‘D’ will always contain Dragon Ball's with the number of stars greater than that of the Dragon Ball ‘D’.

Can you find out how many structurally unique binary trees Gohan can make by fulfilling these conditions?

Note:

The number of structurally unique binary trees can be very large, so return the number of structurally unique binary trees modulo 10^9 + 7.

You are given an integer array 'ARR' of size 'N' and an integer 'S'. Your task is to return the list of all pairs of elements such that each sum of elements of each pair equals 'S'.

Note:

Each pair should be sorted i.e the first value should be less than or equals to the second value. 

Return the list of pairs sorted in non-decreasing order of their first value. In case if two pairs have the same first value, the pair with a smaller second value should come first.