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Print Series

Easy

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Average time to solve is 10m

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Problem statement

You have given two positive integers N and K. Your task is to print a series of numbers i.e subtract K from N until it becomes 0 or negative then add K until it becomes N. You need to do this task without using any loop.

For Example:

For  N = 5 , K = 2 
Series = [ 5, 3, 1, -1, 1, 3, 5]

Detailed explanation ( Input/output format, Notes, Images )

Input format :

The first line of input contains a single integer T, representing the number of test cases or queries to be run 

The first line of each test contains two space-separated integers N and K.

Output format :

For each test case, print a single line containing the required series.

Note:

You do not need to print anything, it has already been taken care of. Just implement the given function.

Constraints :

1 <= T <= 100   
1 <= N <= 3000 
1 <= K <= N 

Time Limit: 1sec

Sample Input 1 :

2 
3 2
5 4

Sample Output 1 :

3 1 -1 1 3
5 1 -3 1 5

Explanation For Sample 1:

For the 1st test case:
The numbers in the sequence are 3, 3 - 2, 3 - 2 - 2, 3 - 2 - 2 + 2, 3 - 2 - 2 + 2 + 2, which is the same as 3, 1, -1, 1, 3. 

For the 2nd test case:
The numbers in the sequence are 5, 5 - 4, 5 - 4 - 4, 5 - 4 - 4 + 4, 5 - 4 - 4 + 4 + 4, which is the same as 5, 1, -3, 1, 5.

Sample Input 2 :

1
4 2

Sample Output 2 :

4 2 0 2 4

Hint 1

Think of a solution using recursion.

Approaches (1)

Approach 1

Recursion

The idea here is to use recursion,we can print current N two times in the current recursion stack. One for decreasing order and one for increasing order.

Steps :

Declare an empty array to store our series, say answer.
Define and call function series(answer, N, K), where N, and K is the given number.
At last return answer.

void series(answer, N, K):

Add N to answer.
Base condition, if N equals to 0 or negative then return.
Recur for series(answer, N - K, K).
Add N to answer.

Time Complexity

O(N), where N is the given number.

In the worst case when K = 1 we need to recur for O(N) times. Hence the overall complexity will be O(N).

Space Complexity

O(N), where N is the given number.

In the worst case, when K = 1 we need O(N) recursion calls. Hence the overall complexity will be O(N).

(100% EXP penalty)

Print Series

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