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++ (GCC 9.2.1) (judge verdict: Runtime Error)

#include<bits/stdc++.h>

#define  ll         long long
#define  llu        unsigned long long
#define  mod        1000000007
#define  pi         ((2.0)*acos(0.0))
#define  pb         push_back
#define  pf         push_front
#define  eb         emplace_back
#define  mp         make_pair
#define  all(x)     (x).begin(),(x).end()
#define  X          first
#define  Y          second

/*loop*/
#define  fr(i,m,n)   for(ll i=m;i<n;++i)

/*output shortcuts*/
#define  nl         "\n"
#define  Yes        cout<<"Yes\n"
#define  yes        cout<<"yes\n"
#define  YES        cout<<"YES\n"
#define  No         cout<<"No\n"
#define  no         cout<<"no\n"
#define  NO         cout<<"NO\n"

using namespace std;
int main()
{
    ios::sync_with_stdio(0);
    cin.tie(0);
    cout.tie(0);

    ll n,w;
    cin>>n>>w;

    vector<ll>dp(w+1, 0);
    fr(i,0,n)
    {
        ll x,val;
        cin>>x>>val;

        for(ll j=w;j>=x;j--)
        {
            dp[j]=max(dp[j], dp[j-x]+val);
        }
    }
    cout<<dp[w]<<nl;
return 0;
}