#include <bits/stdc++.h>
using namespace std;
// #define int long long
#define pii pair<int, int>
#define endl '\n'
#define all(a) a.begin(), a.end()
const int maxi = 2e5 + 10;

int dp[3020][3020][2],p[3010],w[3010][11];
signed main()
{
    ios::sync_with_stdio(false);
    cin.tie(0);
    cout.tie(0);
    
    int t = 1;
    // cin >>t;
    while (t--)
    {
        int n, k;
        cin >> n >> k;
        for (int i = 1; i <= n;i++){
            cin >> p[i];
            for (int j = 1; j <= p[i];j++){
                cin >> w[i][j];
            }
        }
        int ans = 0;
        memset(dp, -1, sizeof(dp));
        dp[0][0][0] = 0;
        for (int i = 0; i < n;i++){
            memcpy(dp[i+1], dp[i], sizeof(dp[i]));
            for (int j = 0; j < k;j++){
                
                if(dp[i][j][0]!=-1){
                    if(j+p[i+1]<=k)
                        dp[i + 1][j + p[i + 1]][0] = max(dp[i + 1][j + p[i + 1]][0], dp[i][j][0] + w[i + 1][p[i + 1]]);
                    for (int q = 1; q < p[i + 1];q++){
                        dp[i+1][j+p[i+1]][1]=max(dp[i+1][j+p[i+1]][1], dp[i][j][0] + w[i + 1][q]);
                    }
                }
                if(dp[i][j][1]!=-1){
                    dp[i + 1][j + p[i+1]][1] = max(dp[i + 1][j + p[i+1]][1], dp[i][j][1] + w[i + 1][p[i + 1]]);
                }
            }
        }
        // cout << dp[3][4][1] << endl;
        for (int i = 0; i <= k; i++)
        {
            ans = max(ans, dp[n][i][0]);
            
        }
        for (int i = k+1; i <= k+10; i++)
        {
            ans = max(ans, dp[n][i][1]);
            
        }
        cout << ans << endl;
    }   
}