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: Wrong Answer)

#include <bits/stdc++.h>
#define fin freopen("input", "r", stdin);
#define fout freopen("output", "w", stdout);
#define wt(x) cerr << #x << ": " << x << " ";
#define whatis(x) {cerr << #x << ": " << x << endl;}
#define whatis2(x, y) {wt(x); wt(y); cerr << endl;}
#define whatis3(x, y, z) {wt(x); wt(y); wt(z); cerr << endl;}
#define whatis4(x, y, z, a) {wt(x); wt(y); wt(z); wt(a); cerr << endl;}
using namespace std;

typedef long long ll; typedef unsigned long long ull; typedef long double ld;
const ll MOD = 1000000007; const ld PI = acos(-1.0);

const int N = (int) 1e2 + 10; // Max number of items
const int W = (int) 1e9 + 10; // Max weight my knapsack can hold
const int V = (int) 1e3 + 10; // Max value
ll dp[N][V * N];
struct ITEM { ll value; ll weight; };
ll n, mx_weight;
ll solve() {
    // dp[i][j] -> i: number of current elements
    // j: max current value
    // dp[i][j] returns the min weight with i elements and j value
    cin >> n >> mx_weight;
    vector<ITEM> items(n + 1);
    ll mx_value = 0;
    for (int i = 1; i <= n; ++i) {
        cin >> items[i].weight >> items[i].value;
        mx_value += items[i].value;
    }
    const int INF = 1e6;
    for (int i = 0; i <= n; ++i) {
        for (int cur_value = 0; cur_value <= mx_value; ++cur_value) {
            dp[i][cur_value] = INF;
        }
    }
    for (int i = 0; i <= n; ++i) dp[i][0] = 0;
    /* for (int cur_value = 0; cur_value <= mx_value; ++cur_value) dp[0][cur_value] = 0; */
    ll ans = 0;
    ll wt = 0;
    for (int i = 1; i <= n; ++i) {
        for (int cur_value = 1; cur_value <= mx_value; ++cur_value) {
            dp[i][cur_value] = dp[i-1][cur_value];
            if (items[i].value <= cur_value) {
                dp[i][cur_value] = min (dp[i-1][cur_value - items[i].value] + items[i].weight,
                        dp[i-1][cur_value]);
            }
            if (dp[i][cur_value] <= mx_weight) ans = max (ans, (ll) cur_value);
        }
    }
    /* whatis(wt); */
    return ans;
}

int main() {
    ios_base::sync_with_stdio(false);
    cin.tie(NULL); cout.tie(NULL);

    cout << solve() << endl;


    return 0;
}