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: Time Limit Exceeded)

    #include <bits/stdc++.h>
    #include <ext/pb_ds/assoc_container.hpp> // Common file
    #include <ext/pb_ds/tree_policy.hpp>
    #include <functional> // for less

    using namespace std;
    #define md 1000000007
    #define itn int
    #define pb push_back
    #define mp make_pair
    // #define ull unsigned long long int
    #define ll long long 
    #define int ll
    #define ppi pair<int, int>
    #define ppl pair<ll, ll>
    #define vi vector<int>
    #define all(x) x.begin(), x.end()
    #define ff first
    #define lb lower_bound
    #define ub upper_bound
    #define ss second
    #define inf 1e9
    #define enld '\n'
    #define cuot cout
    #define trace1(x) cerr << #x << ": " << x << endl
    #define trace2(x, y) cerr << #x << ": " << x << " | " << #y << ": " << y << endl
    #define trace3(x, y, z)                                                        \
      cerr << #x << ":" << x << " | " << #y << ": " << y << " | " << #z << ": "    \
           << z << endl
    #define trace4(a, b, c, d)                                                     \
      cerr << #a << ": " << a << " | " << #b << ": " << b << " | " << #c << ": "   \
           << c << " | " << #d << ": " << d << endl
    #define trace5(a, b, c, d, e)                                                  \
      cerr << #a << ": " << a << " | " << #b << ": " << b << " | " << #c << ": "   \
           << c << " | " << #d << ": " << d << " | " << #e << ": " << e << endl
    #define trace6(a, b, c, d, e, f)                                               \
      cerr << #a << ": " << a << " | " << #b << ": " << b << " | " << #c << ": "   \
           << c << " | " << #d << ": " << d << " | " << #e << ": " << e << " | "   \
           << #f << ": " << f << endl
    #define trace(v)                                                               \
      for (auto it = v.begin(); it != v.end(); it++)                               \
        cerr << *it << " ";                                                        \
      cerr << endl;
    #define linf 1e18
    #define reset(x) memset(x, 0, sizeof(x))
    #define rep(i, a, b) for (int i = a; i < b; i++)

    using namespace __gnu_pbds;

    typedef tree<int, null_type, less<int>, rb_tree_tag,
                 tree_order_statistics_node_update>
        oset;

    void fastio() {
      ios_base::sync_with_stdio(false);
      cin.tie(NULL);
    }
    // int n;
    int w[105],v[105];
    map<pair<int,int>,int> dp;
    map<pair<int,int>,bool> is;
    int go(int i,int wt){
        if(wt<0)return -inf;
        if(i<0)
            return 0;
        if(is[{i,wt}]!=0)return dp[{i,wt}];
        // cout<<i<<" "<<wt<<endl;
        is[{i,wt}]=1;
        return dp[{i,wt}]=max(v[i]+go(i-1,wt-w[i]),go(i-1,wt));
    }

    void solve()
    {
        int n,W;cin>>n>>W;
        rep(i,0,n)cin>>w[i]>>v[i];
        // for(int i=0;i<=n;i++){
        //     for(int j=0;j<=W;j++)dp[i][j]=-1;
        // }
        
        cout<<go(n-1,W);cout<<endl;

        // for(int i=0;i<n;i++){
        //     for(int j=0;j<=W;j++)cout<<dp[i][j]<<" ";cout<<endl;
        // }
    }

    signed main() {
      fastio();
      int t;
      t = 1;
      // cin >> t;
      for (int i = 1; i <= t; i++) {
        // cout << "Case #" << i << ": ";
        solve();
      }
      return 0;
    }