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Points:
15 (partial)

Time limit:
4.0s

Memory limit:
512M

Authors:

Problem types

Allowed languages

Ada, Assembly, Awk, Brain****, C, C#, C++, COBOL, ~~CommonLisp~~, D, Dart, F#, Forth, Fortran, Go, ~~Groovy~~, Haskell, Intercal, Java, JS, Kotlin, Lisp, Lua, ~~Nim~~, ~~ObjC~~, OCaml, ~~Octave~~, Pascal, Perl, PHP, Pike, Prolog, Python, Racket, Ruby, Rust, Scala, Scheme, Sed, Swift, TCL, Text, Turing, VB, Zig

The boolean satisfiability problem is a famous problem in computer science. You are given booleans, and a list of numbers. A boolean is satisfied if a subset from the numbers sum up to less than or equal to . What is the maximum number of booleans that can be satisfied?

Note: the empty subset sums up to 0.

#### Input Specification

On the first line, there are two integers , and , separated by a space.

On the second line is a space separated list of the integers.

Each line is followed by one line feed character (ASCII code 0x0a).

There are no trailing spaces or empty lines.

#### Output Specification

One integer, the number of subsets that sum to less than or equal to .

#### Constraints

For all subtasks:

For all subset sums ,

For 2 of the 15 available marks,

#### Sample Input 1

```
10 10
8 2 10 10 6 1 10 10 1 5
```

#### Sample Output 1

`33`

#### Sample Input 2

```
5 5
1 2 3 4 5
```

#### Sample Output 2

`10`

## Comments