Combinatorial - 0-1 Knapsack Problem

Time Limit : 1 sec, Memory Limit : 65536 KB
Japanese version is here

0-1 Knapsack Problem


You have N items that you want to put them into a knapsack. Item i has value vi and weight wi.

You want to find a subset of items to put such that:

  • The total value of the items is as large as possible.
  • The items have combined weight at most W, that is capacity of the knapsack.

Find the maximum total value of items in the knapsack.

Input

N W
v1 w1
v2 w2
:
vN wN

The first line consists of the integers N and W. In the following lines, the value and weight of the i-th item are given.

Output

Print the maximum total values of the items in a line.

Constraints

  • 1 ≤ N ≤ 100
  • 1 ≤ vi ≤ 1000
  • 1 ≤ wi ≤ 1000
  • 1 ≤ W ≤ 10000

Sample Input 1

4 5
4 2
5 2
2 1
8 3

Sample Output 1

13

Sample Input 2

2 20
5 9
4 10

Sample Output 2

9