SDE - 1

You are given an integer 'N'. For this given integer, find the XOR of all the integers starting from 0 to 'N'.

You have been given an array/list ARR consisting of ‘N’ integers. You are also given a positive integer ‘K’.

Your task is to find the lexicographically smallest ARR that can be obtained by swapping at most K consecutive elements.

An array/list P is lexicographically smaller than its permutation Q if and only if, for the earliest index at which P and Q differ, P's element at that index is smaller than Q's element at that index. Example, P = [1, 12, 4, 7, 8] is lexicographically smaller than Q = [1, 12, 8, 4, 7].

For example, if ARR = [70, 60, 90, 21, 11] and K = 3, then-

Swap 1: We swap adjacent elements 90 and 21. So, ARR after one swap is [70, 60, 21, 90, 11].
Swap 2: We swap adjacent elements 60 and 21. So, ARR after one swap is [70, 21, 60, 90, 11].
Swap 3: We swap adjacent elements 70 and 21. So, ARR after one swap is [21, 70, 60, 90, 11].
The lexicographically smallest ARR after K = 3 swaps is [21, 70, 60, 90, 11].

You are the class teacher and you have a boring duty to get the class arranged according to roll numbers.

There are 'N' students in your class, each student has a roll number between 1 and N. You are also given an array 'ARR' indicating the initial arrangement of the students, and you need to rearrange them so they are sorted by roll number.

In order to make this process more interesting, you come up with an idea! To rearrange the students you can select any student and place him either at the beginning or at the end, and do this until all the students are sorted in increasing order of their roll numbers. You need to find the minimum such steps you need to perform to rearrange the students in increasing order of their roll numbers.

For Example :

If ‘N’ = 5, ‘ARR’ = {1, 2, 4, 5, 3}

You can sort the given arrangement in two steps. 

In the first step select the student with roll number 4 (ARR[2]) and place him at the end, the arrangement now becomes: {1, 2, 3, 5, 3, 4}. In the second step select the student with roll number 5 (ARR[3]) and place him at the end, resulting in the arrangement: {1, 2, 3, 4, 5} which is in sorted order.

It is not possible to sort the given arrangement in less than two steps, therefore we will print 2.

You are given an array consisting of N positive integers, your task is to count the number of distinct possible values that can be obtained by taking the bitwise OR of the elements of all possible subarrays of the given array

Note:

1) A subarray is a part of the array which is contiguous (i.e. elements in the original array occupy consecutive positions) and inherently maintains the order of elements. For example, the subarrays of the array {1, 2, 3} are {1}, {1, 2}, {1, 2, 3}, {2}, {2, 3}, and {3}.
2) Bitwise OR operation takes two numbers and performs OR operation on every bit of those two numbers. For example, consider two numbers 2 and 3 their bitwise OR will be 3. Because the binary representation of 2 is 10 and the binary representation of 3 is 11. And OR of 10 and 11 will be 11 which evaluates to 3.
3) The array may contain duplicate elements.

You are given two big numbers ‘A’ and ‘B’ as strings. Your task is to find the product of both the numbers.

Note:

There are no leading zeros in both the strings, except the number 0 itself.
Do not use any built-in Big Integer Library.

For Example:

If, A = 123, and B = 456.
So the product of both numbers will be 56088.

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