#include<bits/stdc++.h>
using namespace std;



using ll = long long;
void solve() {
    int n , k;
    cin >> n >> k;
    vector<vector<int> > mat(n);
    vector<ll> value(n);
    int mx = 0;
    ll sum = 0;
    for(auto &it : mat) {
        int x;
        cin >> x;
        mx += x;
        it.resize(x);
        for(auto &v : it) cin >> v , sum += v;
    }
    for(int i = 0 ; i < n ; ++i) {
        ll s = 0;
        for(auto it : mat[i]) s += it;
        value[i] = s;
    }
    vector<ll> dp1(k + 1) , dp2;
    for(int i = 0 ; i < n ; ++i) {
        if(i == n - 1) dp2 = dp1;
        int v = mat[i].size();
        ll w = value[i];
        for(int j = k ; j >= v ; --j) {
            dp1[j] = max(dp1[j] , dp1[j - v] + w);
        }
    }
    int w = 0;
    for(int i = k ; i >= 0 ; --i) {
        if(i != 0) {
            if(dp1[i] != dp1[i - 1]) {
                w = i;
                break;
            }
        }
    }
    ll ans = dp1[k];
    if(sum == ans) cout << ans << '\n';
    else {
        cout << ans + k - w << '\n';
    }
}
int main(){
    ios::sync_with_stdio(0);
    cin.tie(0);cout.tie(0);
    solve();
    return 0;
}