Writing Code

题意翻译

## 题目描述： 有 $n$ 个程序员，每个程序员都可以写任意行代码，总共要编写 $m$ 行代码，这 $m$ 行代码可以由多个程序员来编写。但是第 $i$ 个程序员在一行代码中会出现 $a_i$ 个 bug。现在希望知道有多少种方案能使得这 $m$ 行代码中的 bug 的数量不超过 $b$ 个。 两个方案不同当且仅当某个程序员编写的代码量（行数）不同。 ## 输入格式： 输入第一行包含四个整数 $n,m,b,mod$。 接下来一行 $n$ 个整数 $a_i$。 ## 输出格式： 输出一行一个整数，表示 $m$ 行代码 bug 数量不超过 $b$ 的方案数对 $mod$ 取模后的答案。 ## 提示说明： $1 \le n,m \le 500,0 \le b \le 500;1 \le mod \le 10^9+7;0 \le a_i \le 500$ Translated by @Mine_King

题目描述

Programmers 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 $ .

输入输出格式

输入格式

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.

输出格式

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

输入输出样例

输入样例 #1

3 3 3 100
1 1 1

输出样例 #1

10

输入样例 #2

3 6 5 1000000007
1 2 3

输出样例 #2

0

输入样例 #3

3 5 6 11
1 2 1

输出样例 #3

0