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)

# Define Item class
Item = Struct.new(:value, :weight)

def max(a, b)
  a > b ? a : b
end

# Make 2D array
def make_2d_array(n, m, init)
  n.times.map{[init] * m}
end


# Input values
_, W = gets.split(' ').map(&:to_i)
items = []
while line = gets
  v, w = line.split(' ').map(&:to_i)
  items.push(Item.new(v, w))
end


# Create DP table
dp_table = make_2d_array(items.size + 1, W + 1, nil)
# Initialize the first column
dp_table.size.times{|i|
  dp_table[i][0] = 0
}
# Initialize the first row
dp_table[0].size.times{|j|
  dp_table[0][j] = 0
}


# Fill DP table
(1..items.size).each{|i|
  item = items[i-1]
  (1..W).each{|j|
    if 0 <= j - item.weight
      dp_table[i][j] = max(dp_table[i-1][j], dp_table[i-1][j - item.weight] + item.value)
    else
      dp_table[i][j] = dp_table[i-1][j]
    end

  }
}

# Get max weight
max_weight = dp_table[-1][-1]
puts(max_weight)