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.

You may assume 1 ≤ N ≤ 100000.

Input

The first line of the input contains the number of test cases, T.

Each test case begins with a line containing three integers, N, K and P. This is followed by the values of a₁, a₂, ..., a_N, one per line.

Output

Output one line per test case, containing the smallest partial sum modulo P that is at least K, as described above.

Example

Input:
1
7 2 17
12
13
15
11
16
26
11

Output:
2