Overview

Given the compensation amounts of \(N\) employees, the problem asks to find the sum of compensation amounts for employees whose compensation is a multiple of \(K\).

Analysis

Problem Breakdown

What this problem requires can be broken down into 2 steps: 1. Determine whether each employee’s compensation \(P_i\) is a multiple of \(K\) 2. Sum up all compensation amounts that satisfy the condition

How to Determine Multiples

Whether a number \(P_i\) is a multiple of \(K\) can be determined using the remainder (modulo).

If the remainder when dividing \(P_i\) by \(K\) is \(0\), then \(P_i\) is a multiple of \(K\).

For example, when \(K = 3\): - \(P_i = 6\) → \(6 \div 3 = 2\) remainder \(0\) → multiple of \(K\) - \(P_i = 7\) → \(7 \div 3 = 2\) remainder \(1\) → not a multiple of \(K\)

Why This Approach Is Sufficient

A straightforward approach of “checking each employee one by one” is sufficient.

• The number of employees \(N\) is at most \(2 \times 10^5\)
• For each employee, we only perform a multiple check (one division operation)
• This totals about \(2 \times 10^5\) calculations, which fits within the time limit

No special techniques or algorithms are needed; this can be solved with a simple brute-force search.

Algorithm

1. Read \(N\) and \(K\) from input
2. Read the list of compensation amounts \(P\) from input
3. Initialize the sum to \(0\)
4. For each compensation amount \(P_i\):
   • If \(P_i \mod K = 0\) (\(P_i\) is divisible by \(K\)), add \(P_i\) to the sum
5. Output the final sum

Concrete Example

Sample input: \(N = 5\), \(K = 3\), \(P = [6, 7, 9, 4, 12]\)

Employee	Compensation \(P_i\)	\(P_i \mod 3\)	Multiple of \(K\)?
1	6	0	✓
2	7	1	✗
3	9	0	✓
4	4	1	✗
5	12	0	✓

Sum: \(6 + 9 + 12 = 27\)

Complexity

• Time complexity: \(O(N)\)
  • For each of the \(N\) employees, we perform a multiple check (constant time) and addition
• Space complexity: \(O(N)\)
  • Required to store the list of compensation amounts

Implementation Notes

• Modulo operator %: In Python, p % K == 0 can determine whether \(p\) is a multiple of \(K\)

• Generator expression: Writing sum(p for p in P if p % K == 0) allows you to concisely express the sum of elements satisfying the condition in one line

• When no employees qualify: If no employees satisfy the condition, sum() automatically returns \(0\), so no special handling is needed

  Source Code

N, K = map(int, input().split())
P = list(map(int, input().split()))

total = sum(p for p in P if p % K == 0)
print(total)

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