Problem 1: Best Sums, (R Shreevatsa, CMI)
Given a sequence of positive integers a1, a2, …, aN, and 1 ≤ i ≤ j ≤ N, the partial sum from i to j is ai + ai+1 + … + aj.
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
7 2 17 12 13 15 11 16 26 11
Sample Output
2