Problem7163--ABC251 —— B - At Most 3 (Judge ver.)

7163: ABC251 —— B - At Most 3 (Judge ver.)

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Time Limit : 1.000 sec  Memory Limit : 256 MiB

Description

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?

Input

Input is given from Standard Input in the following format:
$N\ W$
$A_1\ A_2\ \dots\ A_N$

Output

Print the answer.

Constraints

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

Sample 1 Input

2 10
1 3

Sample 1 Output

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 2 Input

2 1
2 3

Sample 2 Output

0
There are no good integers less than or equal to W.

Sample 3 Input

4 12
3 3 3 3

Sample 3 Output

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.

7 251
202 20 5 1 4 2 100

48

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