Problem: You have N items that you want to put them into a knapsack. Item i has value vi and weight wi.

You want to find a subset of items to put such that:

* The total value of the items is as large as possible.
* The items have combined weight at most W, that is capacity of the knapsack.



Find the maximum total value of items in the knapsack.

Constraints

* 1 ≤ N ≤ 100
* 1 ≤ vi ≤ 100
* 1 ≤ wi ≤ 10,000,000
* 1 ≤ W ≤ 1,000,000,000

Input


N W
v1 w1
v2 w2
:
vN wN


The first line consists of the integers N and W. In the following N lines, the value and weight of the i-th item are given.

Output

Print the maximum total values of the items in a line.

Examples

Input

4 5
4 2
5 2
2 1
8 3


Output

13


Input

2 20
5 9
4 10


Output

9

Solution (in CPP):

Solution:
#include<iostream>
#include<algorithm>
using namespace std;

#define INF 100000001

int main(){
    int N,W; cin >> N >> W;
    int v[N],w[N]; 
    int sum_v(0);
    for(int i=0;i<N;i++){
        cin >> v[i] >> w[i];
        sum_v += v[i];
    }

    int DP[N+1][sum_v+1];
    
    DP[0][0] = 0;
    for(int j=1;j<=sum_v;j++){
        DP[0][j] = INF;
    }
    
    for(int i=1;i<=N;i++){
        for(int j=0; j<=sum_v; j++){
            if(j<v[i-1]){
                DP[i][j] = DP[i-1][j];
            }else{
                DP[i][j] = min(DP[i-1][j], DP[i-1][j-v[i-1]]+w[i-1]);
            }
        }
    }

    for(int i=sum_v;i>=0;i--){
        if(DP[N][i]<=W){
            cout << i << endl;
            break;
        }
    }

    return 0;
}