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: Accepted)

#include <bits/stdc++.h>
#include <ext/pb_ds/assoc_container.hpp>
#include <ext/pb_ds/tree_policy.hpp>
using namespace __gnu_pbds;
using namespace std;

template <typename T>
using ordered_set = tree<T, null_type, less<T>, rb_tree_tag, tree_order_statistics_node_update>;
template <typename T>
using ordered_set_rev = tree<T, null_type, greater<T>, rb_tree_tag, tree_order_statistics_node_update>;
template <typename T>
using dijkstra = priority_queue<T, vector<T>, greater<T>>;

using namespace std;
typedef long long ll;
typedef unsigned long long ull;
#define fbo find_by_order //k th index
#define ook order_of_key // strictly smaller than k
#define PI acos(-1.0)
#define inf 0x3f3f3f3f
#define max_ull 18446744073709551615
#define max_ll 9223372036854775807
#define min3(a, b, c) min(a, min(b, c))
#define max3(a, b, c) max(a, max(b, c))
#define min4(a, b, c, d) min(min(a, b), min(c, d))
#define max4(a, b, c, d) max(max(a, b), max(c, d))
#define max5(a, b, c, d, e) max(max3(a, b, c), max(d, e))
#define min5(a, b, c, d, e) min(min3(a, b, c), min(d, e))
#define lead_zero(x) __builtin_clzll(x)
#define trail_zero(x) __builtin_ctzll(x)
#define total_1s(x) __builtin_popcountll(x)
#define first_1(x) __builtin_ffsll(x)
#define log2_(x) __builtin_clz(1) - __builtin_clz(x)
#define isLeap(x) ((x % 400 == 0) || (x % 100 ? x % 4 == 0 : false))
#define QUERY int test;scanf("%d", &test);for (int _T = 1; _T <= test; _T++)
#define FAST ios_base::sync_with_stdio(0), cin.tie(0)
#define all(v) v.begin(), v.end()
#define reunique(v) v.resize(std::unique(all(v)) - v.begin())
#define pii pair<int, int>
#define pll pair<ll, ll>
#define ff first
#define ss second
#define MERGE(v1, v2, v) merge(all(v1), all(v2), back_inserter(v))
#define MP make_pair
#define EB emplace_back
#define read freopen("input.txt", "r", stdin)
#define write freopen("output.txt", "w", stdout)
#define in_range(v, r, l) upper_bound(all(v), r) - lower_bound(all(v), l)
#define LCM(a,b) (a/__gcd(a,b))*b;
ll rdn(int y, int m, int d) {
    /* Rata Die day one is 0001-01-01 */
    if (m < 3)
        y--, m += 12;
    return 365 * y + y / 4 - y / 100 + y / 400 + (153 * m - 457) / 5 + d - 306;
}
/* Direction arrays */
/* int dx[] = {1,-1,0,0}, dy[] = {0,0,1,-1}; */                        // 4 Direction
/*int dx[] = {1,-1,0,0,1,1,-1,-1}, dy[] = {0,0,1,-1,1,-1,1,-1};       */ // 8 Direction
/* int dx[] = {1,-1,1,-1,2,2,-2,-2} , dy[] = {2,2,-2,-2,1,-1,1,-1}; */ // Knight Direction
/* int dx[] = {2,-2,1,1,-1,-1} , dy[] = {0,0,1,-1,1,-1}; */            // Hexagonal Direction
/* int dx[] = {2,-2,1,1,-1,-1} , dy[] = {0,0,1,-1,1,-1}; */            // Hexagonal Direction
/* int day[] = {31, 28, 31, 30, 31, 30, 31, 31, 30, 31, 30, 31}; */
const int N=1e3;
ll dp[N*100+9];
ll ww[104];
ll val[104];
int main() {
    ll w;
    int n;
    scanf("%d %I64d",&n,&w);
    ll maxval=0;
    for(int i=0;i<n;i++){
        scanf("%I64d %I64d",&ww[i],&val[i]);
        maxval+=val[i];
    }
    memset(dp,inf,sizeof dp);
    dp[0]=0;
    for(int i=0;i<n;i++){
        for(int j=maxval;j>=val[i];j--){
            dp[j]=min(dp[j],ww[i]+dp[j-val[i]]);
        }
    }
    ll ans=0;
    for(ll i=0;i<=maxval;i++){
        if(dp[i]<=w){
            ans=max(ans,i);
        }
    }
    cout<<ans<<endl;
}