HardDynamic Programming2000 ms256 MB

Certification Roadmap

Given module study times and readiness values, choose modules whose total time is at most `T` and maximize total readiness.

Statement

Given module study times and readiness values, choose modules whose total time is at most `T` and maximize total readiness.

Input

First line: `n T`. Next `n` lines: `time readiness`.

Output

Print the maximum readiness value.

Constraints

  • `1 <= n <= 100`, `1 <= T <= 10000`

Examples

Example 1

Input

3 5
2 10
3 14
4 16

Output

24

Choose the first two modules for total time 5 and readiness 24.

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