Maximum Pairwise Modular Sum CodeChef Solution | CodeChef Problem Solution 2022

[Solution] Maximum Pairwise Modular Sum CodeChef Solution | CodeChef Problem Solution 2022

You are given an array A$A$ containing N$N$ integers, and a positive integer M$M$. Find the maximum value of

Ai+Aj+((Ai−Aj)modM)$$A_i+A_j+((A_i-A_j)modM)$$

across all pairs 1≤i,j≤N$1\le i,j\le N$.

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Note that xmodM$xmodM$ refers to the smallest non-negative integer obtained as the remainder upon dividing x$x$ by M$M$. For example, 4mod3=1$4mod3=1$ and (−10)mod3=2$(-10)mod3=2$.

Input Format

• The first line of input will contain a single integer T$T$, the number of test cases. The description of test cases follows.
• Each test case consists of two lines of input.

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• The first line of each test case contains two space-separated integers N$N$ and M$M$.
• The second line of each test case contains N$N$ space-separated integers A1,A2,…,AN$A_1,A_2,\dots ,A_N$.

Output Format

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• For each test case, output on a new line the maximum value of Ai+Aj+((Ai−Aj)modM)$A_i+A_j+((A_i-A_j)modM)$.

Constraints

• 1≤T≤100$1\le T\le 100$
• 2≤N≤2⋅105$2\le N\le 2\cdot {10}^5$
• 2≤M≤5⋅108$2\le M\le 5\cdot {10}^8$
• 0≤Ai≤5⋅108$0\le A_i\le 5\cdot {10}^8$
• The sum of N$N$ across all test cases won't exceed 2⋅105$2\cdot {10}^5$.

Subtasks

• Subtask 1 (10 points):
  • The sum of N$N$ across all test cases won't exceed 1000$1000$
• Subtask 2 (20 points):
  • 2≤M≤1000$2\le M\le 1000$
• Subtask 3 (70 points):
  • Original constraints

Solution Click Below:-  CLICK HERE