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?

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

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

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

见题面 Input 部分

见题面 Output 部分