#define _CRT_SECURE_NO_WARNINGS 1
#include<bits/stdc++.h>
#include<unordered_map>
#include<unordered_set>
using namespace std;
#define double long double
//#define int long long
#define lc u<<1
#define rc u<<1|1
#define endl "\n"
#define X first
#define Y second
typedef unsigned long long ull;
typedef long long ll;
typedef pair<int, int> PII;
const ll N = 3e3 + 5;
const ll maxm = 2e18;
const ll mod = 1e9 + 7;

ll exgcd(ll a, ll b, ll& x, ll& y);

ll p[N];
ll a[N][15];
ll n, k;
ll dp[N][N];

void solve() {
    cin >> n >> k;
    ll ans = 0;
    for (int i = 1; i <= n; i++) {
        cin >> p[i]; a[i][0] = 0;
        for (int j = 1; j <= p[i]; j++) {
            cin >> a[i][j]; a[i][j] += a[i][j - 1];
        }
    }
    for (int i = 1; i <= n; i++) {//枚举物品
        for (int j = 0; j < k; j++) {//枚举过去的状态，
            //更新新的状态，但是新的状态不能被当前状态继承到
            //我们应该开二维，9e6,好像开不出来,唉开出来，mle再改滑动数组
            dp[i][j] = max(dp[i][j], dp[i - 1][j]);
            if (j + p[i] <= k) {
                dp[i][j + p[i]] = max(dp[i][j + p[i]], dp[i - 1][j] + a[i][p[i]]);
            }
            else {
                dp[i][k] = max(dp[i][k], dp[i - 1][j] + a[i][k-j]);
            }
            dp[i][j + 1] = max(dp[i][j], dp[i][j + 1]);
        }
    }
    cout << dp[n][k] << endl;
    return;
}

signed main() {
    ios::sync_with_stdio(0);
    cin.tie(0), cout.tie(0);
    ll t = 1;//cin >> t;
    while (t--)solve();
    return 0;
}
/*PonyHex*/


ll exgcd(ll a, ll b, ll& x, ll& y) {
    if (b == 0) {
        x = 1; y = 0;
        return a;
    }
    ll g = exgcd(b, a % b, x, y);
    ll temp = x;
    x = y;
    y = temp - (a / b) * y;
    return g;
}

/*
ll ksm(ll a, ll b) {
    ll base = a;
    ll ans = 1;
    while (b) {
        if (b & 1)ans *= base;
        base *= base;
        b >>= 1;
    }
    return ans;
}*/
/*
ll gcd(ll a, ll b) {
    return b ? gcd(b, a % b) : a;
}*/