There are n type of items, ith type item has the weight of wi, value of vi, and a quantity of ai. You can choose an arbitrary number items as long as their weight doesn't exceed a given S. Find a way of choosing items so that their value is maximum possible.
### Input
- First line contains 2 integers n and S.
- Each line in the next n line contains three integers wi,vi,ai.
### Output
- The maximum possible value you can obtain.
### Constraints
- 1≤n≤100,S≤104.
- 1≤wi,vi,ai≤104.
### Example
Input:
34142272361
Output:
15