Knapsack 2

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Points: 7 (partial)
Time limit: 1.0s
Memory limit: 256M

Problem type

These problems are from the atcoder DP contest, and were transferred onto DMOJ. All problem statements were made by several atcoder users. As there is no access to the test data, all data is randomly generated. If there are issues with the statement or data, please contact Rimuru or Ninjaclasher on slack.

There are N items, numbered 1, 2, \dots, N. For each i (1 \le i \le N), item i has a weight of w_i and a value of v_i.

Taro has decided to choose some of the N items and carry them home in a knapsack. The capacity of the knapsack is W, which means that the sum of the weights of items taken must be at most W.

Find the maximum possible sum of the values of items that Taro takes home.

Constraints

  • All values in input are integers.
  • 1 \le N \le 100
  • 1 \le W \le 10^9
  • 1 \le w_i \le W
  • 1 \le v_i \le 10^3

Input Specification

The first line of input will contain 2 space separated integers, N and W.

The next N lines will contain 2 space separated integers, w_i and v_i, the weight and value of item i.

Output Specification

You are to output a single integer, the maximum possible sum of the values of items that Taro takes home.

Sample Input 1

3 8
3 30
4 50
5 60

Sample Output 1

90

Sample Input 2

1 1000000000
1000000000 10

Sample Output 2

10

Sample Input 3

6 15
6 5
5 6
6 4
6 6
3 5
7 2

Sample Output 3

17

Sample Explanations

For the first sample, items 1 and 3 should be taken. Then, the sum of the weights IS 3 + 5 = 8, and the sum of the values is 30 + 60 = 90.

For the third sample, items 2, 4, and 5 should be taken. Then, the sum of the weights is 5 + 6 +3 = 14, and the sum of the values is 6 + 6 + 5 = 17.


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