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: Runtime Error)

#include <bits/stdc++.h>
#include <ext/pb_ds/assoc_container.hpp>
#include <ext/pb_ds/tree_policy.hpp>
#define fast_cin() ios_base::sync_with_stdio(false); cin.tie(NULL)
#define ll long long
#define ld long double
#define mp make_pair
#define pb push_back
#define fi first
#define se second
#define gcd __gcd
#define pcount __builtin_popcount
#define pcountll __builtin_popcountll
#define nxtperm next_permutation
#define int ll
//primitive roots: 998244353 - 3; 7340033 - 5
//#pragma 03
//#pragma GCC target ("sse4.2")

const ll mod = 1000000007;		const double PI = acos(-1.);
using namespace std;
using namespace __gnu_pbds;
typedef tree<int, null_type, less<int>,rb_tree_tag, tree_order_statistics_node_update> ordered_set;
typedef pair<int, int> ii;
typedef vector<int> vi;
typedef vector<ii> vii;
typedef complex<double> cd;

struct custom_hash
{
    static uint64_t splitmix64(uint64_t x)
	{
        x += 0x9e3779b97f4a7c15;
        x = (x ^ (x >> 30)) * 0xbf58476d1ce4e5b9;
        x = (x ^ (x >> 27)) * 0x94d049bb133111eb;
        return x ^ (x >> 31);
    }

    size_t operator()(uint64_t x) const
	{
        static const uint64_t kawaii = chrono::steady_clock::now().time_since_epoch().count();
        return splitmix64(x + kawaii);
    }
};

int const maxn = 200; 
int n, W, v[maxn], w[maxn], dp[maxn][100005]; // minimum weight to reach value j for first i items. 
int mx; 

signed main()
{
//	freopen("in.txt", "r", stdin); freopen("out.txt", "w", stdout);
// 	fast_cin();
	cin >> n >> W;
	for(int i=1;i<=n;i++) cin >> w[i] >> v[i], mx += v[i];  
	for(int i=1;i<=mx;i++) dp[0][i] = 1e18; 
	for(int i=1;i<=n;i++) 
	{
		for(int j=1;j<=mx;j++)
		{
			dp[i][j] = min(dp[i-1][j], dp[i-1][j - v[i]] + w[i]); 
		}
	}
	for(int i=mx;i>=0;i--) 
	{
		if(dp[n][i] <= W)
		{
			cout << i; 
			return 0; 
		} 
	}
}

/*
	Test input:
*/