Indian National Olympiad in Informatics

Related:

Online Programming Contest, 15-16 July 2006

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Advanced Division

Problem 1: Best Sums, (R Shreevatsa, CMI)

Given a sequence of positive integers a₁, a₂, …, a_N, and 1 ≤ i ≤ j ≤ N, the partial sum from i to j is a_i + a_i+1 + … + a_j.

In this problem, you will be given such a sequence and two integers P and K. Your task is to find the smallest partial sum modulo P that is at least K.

For example, consider the following sequence of integers:

    12     13     15     11     16     26     11

Here N = 7. Suppose K = 2 and P = 17. Then, the answer is 2 because 11+16+26 = 53 and 53 mod 17 is 2. On the other hand, if K = 0 the answer is 0 since 15 + 11 + 16 + 26 = 68 and 68 mod 17 is 0.

Input format

The first line contains three integers N, K and P. This is followed by N lines each containing a single integer.

Output format

A single integer indicating the minimum possible segment sum modulo P that is at least K.

Test Data:

You may assume 1 ≤ N ≤ 100000.

Example:

Here is the sample input and output corresponding to the example above.

Sample Input

Sample Output