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 <stack>
#include <queue>
#include <map>
#include <set>
#include <vector>
#include <random>
#include <cmath>
#include <chrono>
#include <cstring>
#include <algorithm>
#include <string>
#include <iostream>
#include <cstdio>
#include <cstring>
#include <cassert>
using namespace std;
using LL = long long;
#define int long long 
#define eps 1e-8
#define fi first
#define se second
#define eb emplace_back
#define close std::ios::sync_with_stdio(false),cin.tie(nullptr),cout.tie(nullptr)
#define FOR(i, x, y) for (LL i = (x), _##i = (y); i < _##i; ++i)
#define FORD(i, x, y) for (LL i = (x), _##i = (y); i > _##i; --i)
#define SORT_UNIQUE(c) (sort(c.begin(),c.end()), c.resize(distance(c.begin(),unique(c.begin(),c.end()))))
#define CASET int ___T; scanf("%d", &___T); for(int __CS=1;__CS<=___T;__CS++)
typedef long long ll;
typedef vector<int> vi;
typedef pair<int,int> pii;
mt19937 dlsrand(random_device{}());
mt19937 mrand(std::chrono::system_clock::now().time_since_epoch().count()); 
int rnd(int x) { return mrand() % x;}
LL bin(LL x, LL n, LL MOD) {LL ret = MOD != 1;for (x %= MOD; n; n >>= 1, x = x * x % MOD)if (n & 1) ret = ret * x % MOD;return ret;}
inline LL get_inv(LL x, LL p) { return bin(x, p - 2, p); }
const double PI = acos(-1.0);
constexpr int maxn = 1e6+10;
constexpr int INF = 0x3f3f3f3f;
constexpr ll linf = 0x3f3f3f3f3f3f3f3f;
constexpr int mod = 1e9+7;
int v[maxn], w[maxn], dp[maxn], N , V;
int32_t main()
{
    cin >> N >> V;
    for(int i = 1; i <= N; i++){
        cin >> v[i] >> w[i];
    }
    memset(dp , 0x3f, sizeof dp);
    dp[0] = 0;
    int zz = 0;
    for(int i = 1; i <= N; i++){
        for(int j = zz + w[i]; j >= w[i]; j--){
            dp[j] = min(dp[j], dp[j-w[i]]+v[i]);
        }
        zz+=w[i];
    }
    for(int i = zz;  i>=0; i--){
        dp[i] = min(dp[i],dp[i+1]);
    }
    int ans = 0;
    // for(int i = 1; i<= V;i++){
    //     printf("dp[%lld]===%lld\n",i,dp[i]);
    // }
    while(dp[ans] <= V)ans++;
    cout << ans - 1;
}