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: Time Limit Exceeded)

//                   ********** YATIN KWATRA **********

// AC BAKSHI RABBA

#include <bits/stdc++.h>
#define ll                      long long 
#define ld                      long double
#define ull                     unsigned long long 
#define FIO                     ios_base::sync_with_stdio(false);cin.tie(NULL);cout.tie(NULL);
#define endl                    "\n"
#define fo(i,a,b)               for(int i = a; i<=b ; i++)
#define rfo(i,a,b)              for(int i = a; i>=b ; i--)
#define vii                     vector<int>
#define vll                     vector<ll>
#define pq                      priority_queue
#define uom                     unordered_map                
#define all(v)                  v.begin(),v.end()
#define mp                      make_pair
#define pb                      push_back
#define pob                     pop_back
#define ff                      first
#define ss                      second
#define pii                     pair<int,int> 
#define pll                     pair<long,long>
#define mll                     map<ll,ll>
#define mii                     map<int,int>
#define vvii                    vector<vii>
#define vvll                    vector<vll>
#define mod                     1000000007
#define pi                      3.1415926535897932384626433832795

using namespace std;

void INPUT() 
{  
    #ifndef ONLINE_JUDGE
    freopen("input.txt", "r", stdin);
    freopen("output.txt", "w", stdout);
    #endif
}

/*
    
   -> Check For Overflows
   -> Out of Bounds
   -> Initialisations of global arrays and variables
   -> Its not Always Complex, Try to simplify
   -> write it down and try to solve
   -> Have Faith in urself and in ur approach
   -> If it seems totally out of reach, switch to next :)
   -> And Come Back later, if possible ..
*/

const int W = 100005;
const int N = 105;

map<pll,ll>dp;
ll n,w;
pll v[N];

ll f(ll i, ll c)
{
  if(i == n or c == 0) return 0LL;

  if(dp.count(mp(i,c))) return dp[mp(i,c)];

  ll op1 = 0, op2 = 0;

  if(c >= v[i].ff)
  {
    op1 = v[i].ss + f(i+1,c-v[i].ff);
    op2 = f(i+1,c);
  }

  dp[mp(i,c)] = max(op1,op2);

  return dp[mp(i,c)];
}

void solve()
{ 
  
        cin >> n >> w;

        dp.clear();
        
        fo(i,0,n-1) cin >> v[i].ff >> v[i].ss;

        sort(v,v+n);

      

        cout << f(0,w) << endl;

       
}
int main() {
    
    FIO
    INPUT();
    
    int t;
    t = 1;
    //cin >> t;
    
    while(t--)
    {
       solve();
    }
    return 0;
}