#include <bits/stdc++.h>
using namespace std;
using i64 = long long;
void solve() {
    int n,k;
    cin >> n >> k;
    vector w(n,vector<int>(1));
    i64 ans = 0;
    for ( int i = 0 ; i < n ; i++ ) {
        cin >> w[i][0];
        ans += w[i][0];
        for ( int j = 0 ; j < w[i][0] ; j++ ) {
            int x;
            cin >> x;
            w[i].emplace_back(x);
        }
    }
    vector dp(2,vector<i64>(2*k+2));
    // 0, k, k+1, 2k+1;
    int cur = 0;
    for ( int i = 0 ; i < n ; i++ ) {
        cur ^= 1;
        for ( int j = 1 ; j <= w[i][0] ; j++ ) {
            for ( int z = k ; z >= 0 ; z-- ) {
                if ( z < j ) break;
                if ( j != w[i][0] ) {
                    dp[cur][k+1+z] = max(dp[cur^1][z-j]+w[i][j],dp[cur][k+1+z]);
                } else {
                    dp[cur][z] = max(dp[cur^1][z-j],dp[cur][z]);
                }
            }
        }
        for ( int j = 0 ; j < 2*k+2 ; j++ ) {
            dp[cur^1][j] = 0;
        }
    }
    i64 mx = 0;
    for ( int j = 0 ; j < 2*k+2 ; j++ ) {
        mx = max(mx,dp[cur][j]);
    }
    cout << ans+mx << '\n';
}
int main() {
    int T = 1;
    // cin >> T;
    while ( T-- ) {
        solve();
    }
}