At Most 3 (Judge ver.)

AtCoder

IDabc251_b

Time2000ms

Memory256MB

Difficulty—

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: $N$ $W$ $A_1$ $A_2$ $\dots$ $A_N$ [samples]

Samples

Input #1

2 10
1 3

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 $3$.

Input #2

2 1
2 3

Output #2

0

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

Input #3

4 12
3 3 3 3

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.

Input #4

7 251
202 20 5 1 4 2 100

Output #4

API Response (JSON)

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      "content": "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 satisf",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
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      "memory_limit": 262144
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    "difficulty": "None",
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    "sign": "abc251_b"
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      "statement_type": "Markdown",
      "content": "There are $N$ weights called Weight $1$, Weight $2$, $\\dots$, Weight $N$. Weight $i$ has a mass of $A_i$.  \nLet us say a positive integer $n$ is a **good integer** if the following condition is satisf...",
      "is_translate": false,
      "language": "English"
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}

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