Problem:
Score : 100 points

Problem Statement

There are N items, numbered 1, 2, \ldots, N.
For each i (1 \leq i \leq 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 \leq N \leq 100

1 \leq W \leq 10^9

1 \leq w_i \leq W

1 \leq v_i \leq 10^3

Input

Input is given from Standard Input in the following format:

N W
w_1 v_1
w_2 v_2
:
w_N v_N

Output

Print 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

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.

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

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.

Solution in Ruby (2.7.1) (judge verdict: Accepted)

def gs() gets.chomp end
def gi() gets.to_i end
def gsmi() gets.chomp.split.map(&:to_i) end
def ang(n) Array.new(n){gsmi} end
def debug(k,v) puts "#{k}: #{v}" end
def desc(ar) ar.sort!{|x,y|y<=>x} end
def min(a,b) a<=b ? a : b end
def max(a,b) a>=b ? a : b end
def sum(ar) ar.inject(:+) end

def arrays(n,num) #要素数、配列数
  ret = Array.new(num){Array.new(n)}
  n.times do |i|
    ins = gsmi
    num.times{|j| ret[j][i] = ins[j] }
  end
  ret
end
inf = Float::INFINITY
$stdin = File.open('input.txt') if File.exist?('input.txt')
n,w_max = gsmi #100, 10**9
ws,vs = arrays(n,2) #w, 10**5
ws.unshift 0
vs.unshift 0

v_max = 100001
dp = Array.new(n+1) do
  [inf] * (v_max + 1)
end
dp[0][0] = 0
(1..n).each do |i|
  v_max.times do |j|
    if(j-vs[i]>=0)
      #puts vs[i] if i==1 && j==1
      dp[i][j] = min(dp[i-1][j], dp[i-1][j-vs[i]]+ws[i])
    else
      dp[i][j] = dp[i-1][j]
    end
    #dp[i][j] = dp[i-1][j] if dp[i][j] > dp[i-1][j]
  end
end

(v_max-1).downto(0) do |j|
  if dp[-1][j]<=w_max
    puts j
    exit
  end
end