Specialist Programmer

You have 'N' chocolates and 'K' empty bags. Your task is to pack all the chocolates in these bags such that any bag can have any number of chocolates, but no bag remains empty. Please note that all the chocolates are different, i.e., they can be numbered from 1 to 'N', but all bags are identical.

E.g., If there are 3 chocolates and 2 bags, then you can pack the chocolates in the following three ways -

[1, 2] and [3].
[2, 3] and [1].
[1, 3] and [2].

Only the above three packings are considered valid. Some more packages are possible; for example, packing [{2}, {3, 1}] is not taken because [{1, 3}, {2}] is already considered, i.e., order of bags and the order of chocolates inside a bag don't matter.

You are given the number of chocolates 'N' and the number of bags 'K'. Find the number of ways to pack the chocolates. Return your answer modulo 10^9+7.

You are given two integers ‘M’ and ‘N’. Your task is to find the number of a unique beautiful array of length ‘M’.

The array of length ‘M’ is said to be beautiful if -

The array consists of elements from 1 to ‘N’.

The array contains at least one ‘N’ length strictly increasing subsequence.

Note:

A subsequence of an array is an ordered subset of the array's elements having the same sequential ordering as the original array. For example, the subsequences of the array  [1, 2, 3] are [1], [2], [3], [1, 2], [1, 3], [2, 3] and [1, 2, 3] where  [2, 1], [3,2, 1] are not subsequence of array [1, 2, 3]

The longest increasing subsequence of an array of numbers is the longest possible subsequence that can be created from its elements such that all elements are in strictly increasing order.

For example:

For M = 3 and N = 2
array : [ 1, 1, 2 ] [ 1, 2, 1 ] [ 1, 2, 2 ] [ 2, 1, 2 ] are beautiful.

array:  [ 1, 1, 1 ] [ 2, 1, 1 ] [ 2, 2, 1 ] [ 2, 2, 2 ] are not beautiful. 

You have been given an array 'A' of N integers. You need to find the maximum value of j - i subjected to the constraint of A[i] <= A[j], where ‘i’ and ‘j’ are the indices of the array.

For example :

If 'A' = {3, 5, 4, 1}

then the output will be 2.
Maximum value occurs for the pair (3, 4)

You are given an array/list consisting of 0 and 1 only. Your task is to find the sum of the number of subarrays that contains only 1 and the number of subarrays that contains only 0.

An array 'C' is a subarray of array 'D' if 'C' can be obtained from 'D' by deletion of several elements from the beginning and several elements from the end. Example :

Let 'ARR' = [1,0,0] then the possible subarrays of 'ARR' will be: {1}, {0}, {0}, {1,0}, {0,0}, {1,0,0}.

Example

If the given array 'ARR' = [1,0,0,0,1,1,0,1]
Then the number of 1’s subarrays will be 5. [{1},{1},{1},{1,1},{1}]
And the number of 0’s subarrays will be 7. [{0},{0},{0},{0,0},{0,0},{0,0,0},{0}]
So our answer will be 5 + 7 = 12.

A group of N people are seated in chairs numbered 1 to N arranged in a circle. You are given an array A, where A[i-1] represents the jump distance for the person on chair i.

From any chair i, a person can jump A[i-1] chairs in either a clockwise (right) or counter-clockwise (left) direction.

Bob starts at chair X and needs to reach chair Y. Your task is to find the minimum number of jumps required to get from chair X to chair Y. If it's impossible to reach chair Y, return -1.