Score : $200$ points

问题描述

设有 $N$ 个重量，分别称为 Weight $1$、Weight $2$、$\dots$、Weight $N$。其中，Weight $i$ 的质量为 $A_i$。

我们称一个正整数 $n$ 为 好整数 ，如果满足以下条件：

• 我们可以选择 最多3个 不同的重量，使得它们的总质量恰好为 $n$。

请问不大于 $W$ 的好整数有多少个？

以上为通义千问 qwen-max 翻译，仅供参考。

Problem Statement

There are $N$ weights called Weight $1$, Weight $2$, $\dots$, Weight $N$. Weight $i$ has a mass of $A_i$.
Let us say a positive integer $n$ is a good integer if the following condition is satisfied:

• We can choose at most $3$ different weights so that they have a total mass of $n$.

How many positive integers less than or equal to $W$ are good integers?

Constraints

• $1 \leq N \leq 300$
• $1 \leq W \leq 10^6$
• $1 \leq A_i \leq 10^6$
• All values in input are integers.

Input

Input is given from Standard Input in the following format:

$N$ $W$

$A_1$ $A_2$ $\dots$ $A_N$

Output

Print the answer.

Sample Input 1

2 10
1 3

Sample Output 1

3

If we choose only Weight $1$, it has a total mass of $1$, so $1$ is a good integer.
If we choose only Weight $2$, it has a total mass of $3$, so $3$ is a good integer.
If we choose Weights $1$ and $2$, they have a total mass of $4$, so $4$ is a good integer.
No other integer is a good integer. Also, all of $1$, $3$, and $4$ are integers less than or equal to $W$. Therefore, the answer is $3$.

Sample Input 2

2 1
2 3

Sample Output 2

0

There are no good integers less than or equal to $W$.

Sample Input 3

4 12
3 3 3 3

Sample Output 3

3

There are $3$ good integers: $3, 6$, and $9$.
For example, if we choose Weights $1$, $2$, and $3$, they have a total mass of $9$, so $9$ is a good integer.
Note that $12$ is not a good integer.

Sample Input 4

7 251
202 20 5 1 4 2 100

Sample Output 4

48

update @ 2024/3/10 10:42:30