System Engineer

Given an array arr of N integers that may contain duplicate integers. The task is to return the count of subsets of the given array such that each subset contains only distinct elements.

Note:

As the answer can be large, return your answer modulo 10^9  + 7. 

There is a N * N maze in Liones guarded by the demons. Goddess Elizabeth is being trapped by the demons. She is kept at the center of the maze. Prince Meliodas is worried and he wants to save Elizabeth at any cost. He killed all the demons guarding the maze. Only the four corners of the maze are open for Meliodas to enter. The magical spell of the demons guarded the maze is still in effect. Thus, there is a limitation on the movement of Meliodas. At any cell of the maze, he can move exactly X steps in only four directions, i.e. Up, Down, Left, and Right where X is the power of each cell of the maze.

Given an N * N maze of non negative integers, where each integer denotes the power of that cell. You have to find the number of ways in which Meliodas can save goddess Elizabeth.

For example:

An input maze is shown below

Elizabeth is trapped in the green cell and Meliodas can enter the maze from any of the yellow cells.

Given an array of non-negative integers ‘A’ and an integer ‘P’, find the total number of subsequences of ‘A’ such that the product of any subsequence should not be more than ‘P’.

A subsequence is a sequence that can be derived from another sequence by deleting some or no elements without changing the order of the remaining elements.

Note

You need to print your answer modulo 10^9 + 7.

For Example

Let us take  A = [1,2,3] and P = 4. 
All the subsequences not having product more than ‘4’ are {1}, {2}, {3}, {1,2}, {1,3}. Therefore count is equal to ‘5’.

You are given ‘N’ types of umbrellas, where each umbrella can shelter some number of people. Given the number of people each umbrella can shelter in the array “UMBRELLA”, you need to determine the minimum number of umbrellas required to cover exactly ‘M’ people with umbrellas.

Note -

You have an infinite number of umbrellas of each type.
If it is not possible to shelter exactly ‘M’ people then print -1.