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: Wrong Answer)

#include <bits/stdc++.h>
#include <fstream>
#include <iostream>
using namespace std;
#define ll long long int
#define pb push_back
#define mp make_pair
#define maxim INT_MAX
#define fi first
#define se second

/* 1. If you can't keep solution in mind, then visualize it on a paper.
 * 2. Try to identify the type of problem - DP, Greedy, Graph, Constructive,
 * 	  Prefix/Suffix, Difference Array, BIT/Segment Tree, etc.
 * 3. Look at the problems from different perspectives - reverse the problem,
 * 	  add instead of delete (maybe?)
 * 4. Divide difficult solutions into cases and/or sequences.
 * 5. Use math rules to solve Nested Summation.
 * 6. Optimisation problems are generally solved with DP, greedy, binary search or brute-force.
 * 7. Try fixing a solution then proving we can't do better or worse than that.
 * ------------------------------------------------------------------
 */
 ll n,w;
 ll ar[105];
 ll br[105];
int main()
{
    cin>>n>>w;
    ll k=0;
    for(ll i=1;i<=n;i++)
    {
        cin>>ar[i]>>br[i];
        k+=br[i];
    }
    ll dp[k+1];
    for(ll i=1;i<=k;i++)
        dp[i]=LONG_MAX;
    dp[0]=0;
    for(ll i=1;i<=n;i++)
    {
        for(ll j=k;j>=br[i];j--)
        {
            dp[j]=min(dp[j],dp[j-br[i]]+ar[i]);
        }
    }
    for(ll i=k;i>=0;i--)
    {
        if(dp[i]<=w)
        {
            cout<<i;
            return 0;
        }
    }

}