#include <bits/stdc++.h>
using namespace std;
long long ans, N, K, dp[3003];
vector<long long> pot[3003];
void divide(long long l, long long r) {
  if (l == r) {
    for (long long i = 0; i < pot[l].size() && i <= K; ++i)
      ans = max(ans, dp[K - i] + pot[l][i]);
    return;
  }
  long long mid = (l + r) / 2, tmp[3003];
  memcpy(tmp, dp, sizeof(tmp));
  for (long long i = l; i <= mid; ++i)
    for (long long j = K; j >= pot[i].size() - 1; --j)
      dp[j] = max(dp[j], dp[j - pot[i].size() + 1] + pot[i].back());
  divide(mid + 1, r);
  memcpy(dp, tmp, sizeof(dp));
  for (long long i = mid + 1; i <= r; ++i)
    for (long long j = K; j >= pot[i].size() - 1; --j)
      dp[j] = max(dp[j], dp[j - pot[i].size() + 1] + pot[i].back());
  divide(l, mid);
  memcpy(dp, tmp, sizeof(dp));
}
signed main() {
  ios::sync_with_stdio(0);
  memset(dp, -0x3f, sizeof(dp));
  cin >> N >> K;
  for (long long i = 1; i <= N; ++i) {
    pot[i].push_back(0);
    long long S;
    cin >> S;
    for (long long j = 1; j <= S; ++j) {
      long long x;
      cin >> x;
      pot[i].push_back(pot[i].back() + x);
    }
  }
  memset(dp, -0x3f, sizeof(dp));
  dp[0] = 0;
  ans = -1e18;
  divide(1, N);
  cout << ans;
  return 0;
}
