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 C++14 (GCC 5.4.1) (judge verdict: Accepted)

#include <bits/stdc++.h>
#include <ext/pb_ds/assoc_container.hpp>
#include <ext/pb_ds/tree_policy.hpp>

using namespace std;
using namespace __gnu_pbds;

#define DIM 107
#define DIMM 100007
#define INF 1000000009.0
#define X 500007
#define epc 0.0000001
#define pi 3.14159265358979323846
#define MAX 25
#define MODULO 10009
const long double gr=(1+sqrt(5))/2;

typedef int I;
typedef long long ll;
typedef long double ld;
typedef unsigned long long ull;

typedef pair<I,I> pII;
typedef pair<ll,ll> pllll;
typedef pair<ld,ld> pldld;

typedef vector<I> vI;
typedef vector<ll> vll;
typedef vector<pllll> vpllll;

typedef char cr;
typedef string str;

typedef tree<
I,
null_type,
less<I>,
rb_tree_tag,
tree_order_statistics_node_update> mset;

ll n,W,sumv,w[DIM],v[DIM],d[DIM][DIMM],maxv;

int main()
{
    //freopen("suffarray.in", "r", stdin);
    //freopen("suffarray.out", "w", stdout);
    //freopen("input.txt","r",stdin);
    //freopen("output.txt","w",stdout);
    //cout<<"ops"<<endl;

    ios::sync_with_stdio(0);
    cin.tie(0);
    cout.tie(0);

    //ll x1,y1,xs,ys,y1,y2,x3,x4,y3,y4;

    cin>>n>>W;
    for(int i=1;i<=n;i++){
     cin>>w[i]>>v[i];
     sumv+=v[i];
    }

    for(int j=1;j<=sumv;j++)d[0][j]=INF;

    for(int i=1;i<=n;i++){
     for(int j=0;j<=sumv;j++){
      d[i][j]=d[i-1][j];
      if(j>=v[i] && d[i-1][j-v[i]]!=INF)d[i][j]=min(d[i-1][j-v[i]]+w[i],d[i][j]);
     }
    }
    for(int j=0;j<=sumv;j++)if(d[n][j]<=W && j>maxv)maxv=j;
    cout<<maxv<<endl;
}