5

Valid Pairs

Difficulty: EASY
Avg. time to solve
22 min
Success Rate
80%

Problem Statement
Suggest Edit

You are given an array arr of N integers and two integers K and M, you need to return true if the given array can be divided into pairs such that the sum of every pair gives remainder M when divided by K. Otherwise, you need to return false.

Every element of the array should contribute to only one pair, i.e if the array is [3, 0, 0] and K = 2 and M = 1, then you need to return false, as element 3 will make a pair with any one of the 0.

For example: If the given array is [2, 1, 5, 7] and K = 9 and M = 3. Then you need to return true because we can divide the array into two pairs, i.e (2, 1) and (5, 7) whose sums are 3 and 12, which when divided by 9 gives remainder 3, thus it is possible to divide the given array into pairs.

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

Then the T test cases follow.

The first line of each test case contains an integer N, where N is the size of the given array.

The second line contains 'N' single space-separated integers representing the elements of the array.

The third line contains two single space-separated integers K and M.
Output Format :
For each test case, print “True” or “False” in a single line.
Note:
You do not need to print anything. It has already been taken care of. Just implement the given function.
Constraint :
1 <= T <= 10
1 <= N <= 10^5
1 <= arr[i] <= 10^9
1 <= K <= 10^9
0 <= M < K

Time Limit: 1 sec
Sample Input 1:
1
4
2 1 5 7
9 3
Sample Output 1:
True
Explanation for input 1:
Pairs will be (2,1) and (5,7) whose sums are 3 and 12. Which will give remainder 3 when divided by 9.
Sample Input 2:
1
5
6 6 3 0 0
9 3
Sample Output 2:
False
Explanation for Input 2:
As pairs would be {6, 6} and {3, 0}, but second 0 will not be able to make pair with any of the elements, thus it is not possible to make valid pairs.
Want to solve this problem? Login now to get access to solve the problems