## PARTSUM - Partial Sums

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Given a sequence of positive integers a1, a2, ..., aN, and 1 ≤ ijN, 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.

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, ..., aN, 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
```
Warning: large Input/Output data, be careful with certain languages