Problem:
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

Solution in Ruby (judge verdict: Accepted)

def kp(vv, wv, w)
	dp1 = Array.new(w + 1, 0)
	vv.length.times do |i|
		dp2 = dp1.clone
		(w + 1).times do |j|
			if j < wv[i] || dp2[j] > dp2[j - wv[i]] + vv[i]
				dp1[j] = dp2[j]
			else
				dp1[j] = dp2[j - wv[i]] + vv[i]
			end
		end
	end
	return dp1[w]
end

if __FILE__ == $0
	vv = Array.new(0)
	wv = Array.new(0)
	n, w = gets.split.map(&:to_i)
	n.times do
		vi, wi = gets.split.map(&:to_i)
		vv << vi
		wv << wi
	end
	puts("#{kp(vv, wv, w)}")
end