Virtual contest is a way to take part in past contest, as close as possible to participation on time. It is supported only ACM-ICPC mode for virtual contests.
If you've seen these problems, a virtual contest is not for you - solve these problems in the archive.
If you just want to solve some problem from a contest, a virtual contest is not for you - solve this problem in the archive.
Never use someone else's code, read the tutorials or communicate with other person during a virtual contest.

No tag edit access

C. Writing Code

time limit per test

3 secondsmemory limit per test

256 megabytesinput

standard inputoutput

standard outputProgrammers working on a large project have just received a task to write exactly *m* lines of code. There are *n* programmers working on a project, the *i*-th of them makes exactly *a*_{i} bugs in every line of code that he writes.

Let's call a sequence of non-negative integers *v*_{1}, *v*_{2}, ..., *v*_{n} a plan, if *v*_{1} + *v*_{2} + ... + *v*_{n} = *m*. The programmers follow the plan like that: in the beginning the first programmer writes the first *v*_{1} lines of the given task, then the second programmer writes *v*_{2} more lines of the given task, and so on. In the end, the last programmer writes the remaining lines of the code. Let's call a plan good, if all the written lines of the task contain at most *b* bugs in total.

Your task is to determine how many distinct good plans are there. As the number of plans can be large, print the remainder of this number modulo given positive integer *mod*.

Input

The first line contains four integers *n*, *m*, *b*, *mod* (1 ≤ *n*, *m* ≤ 500, 0 ≤ *b* ≤ 500; 1 ≤ *mod* ≤ 10^{9} + 7) — the number of programmers, the number of lines of code in the task, the maximum total number of bugs respectively and the modulo you should use when printing the answer.

The next line contains *n* space-separated integers *a*_{1}, *a*_{2}, ..., *a*_{n} (0 ≤ *a*_{i} ≤ 500) — the number of bugs per line for each programmer.

Output

Print a single integer — the answer to the problem modulo *mod*.

Examples

Input

3 3 3 100

1 1 1

Output

10

Input

3 6 5 1000000007

1 2 3

Output

0

Input

3 5 6 11

1 2 1

Output

0

Codeforces (c) Copyright 2010-2018 Mike Mirzayanov

The only programming contests Web 2.0 platform

Server time: Jul/18/2018 17:46:47 (d1).

Desktop version, switch to mobile version.

User lists

Name |
---|