#include <bits/stdc++.h>
#ifndef LOCAL
#define debug(...) 42
#else
#define debug(...) cerr << "[" << #__VA_ARGS__ << "]:", debug_out(__VA_ARGS__)
#endif
#define rep1(a) for (int i = 0; i < a; i++)
#define rep2(i, a) for (int i = 0; i < a; i++)
#define rep3(i, a, b) for (int i = a; i < b; i++)
#define rep4(i, a, b, c) for (int i = a; i < b; i += c)
#define overload4(a, b, c, d, e, ...) e
#define rep(...) overload4(__VA_ARGS__, rep4, rep3, rep2, rep1)(__VA_ARGS__)

#define pb emplace_back
using namespace std;
template <typename T, typename T2> void cmin(T &x, const T2 &y) {
  x = x < y ? x : y;
}
template <typename T, typename T2> void cmax(T &x, const T2 &y) {
  x = x > y ? x : y;
}
using ll = long long;
using vi = vector<int>;
using pii = pair<int, int>;
template <class T> using vc = vector<T>;
template <class T> using pq = priority_queue<T>;
template <class T> using pqg = priority_queue<T, vector<T>, greater<T>>;
mt19937 rng(time(NULL));
const int inf = 1000000000;
const ll lnf = 1000000000000000000;
#define sz(x) int((x).size())
#define all(x) begin(x), end(x)
#define fi first
#define se second

int n, k;
const int N = 3010;
int dp[N][N];
int pre[N][N];
int suf[N][N];
int p[N];
int a[N][11];
void solve() {
  memset(pre, 0xcf, sizeof pre);
  memset(suf, 0xcf, sizeof suf);
  cin >> n >> k;
  for (int i = 1; i <= n; i++) {
    cin >> p[i];
    for (int j = 1; j <= p[i]; j++) {
      cin >> a[i][j];
    }
  }
  pre[0][0] = 0;
  for (int i = 1; i <= n; i++) {
    memcpy(pre[i], pre[i - 1], sizeof pre[i]);
    for (int j = p[i]; j <= k; j++) {
      cmax(pre[i][j], pre[i - 1][j - p[i]] + a[i][p[i]]);
    }
  }
  suf[n + 1][0] = 0;
  for (int i = n; i >= 1; i--) {
    memcpy(suf[i], suf[i + 1], sizeof suf[i]);
    for (int j = p[i]; j <= k; j++) {
      cmax(suf[i][j], suf[i + 1][j - p[i]] + a[i][p[i]]);
    }
  }
  auto get = [&](int p, int rem) {
    int res = -inf;
    for (int i = 0; i <= rem; i++) {
      cmax(res, pre[p - 1][i] + suf[p + 1][rem - i]);
    }
    return res;
  };
  int ans = 0;
  for (int i = 1; i <= n; i++) {
    for (int j = 1; j <= p[i]; j++) {
      int rem = k - j;
      cmax(ans, a[i][j] + get(i, rem));
    }
  }
  cmax(ans, pre[n][k]);
  cout << ans << "\n";
}

int main() {
  ios::sync_with_stdio(false);
  cin.tie(nullptr);
  int t = 1;
  // cin >> t;
  while (t--) {
    solve();
  }
  return 0;
}