#include <iostream>
#include <algorithm>
#include <vector>
#include <deque>

using namespace std;

struct State;

int n;
int end_time;
int cost;
State* charging;
deque<State*> cq;

struct State {
  vector<int> pat;
  bool wait;
  bool charge;
  int cur;
  int cnt;

  void Init() {
    pat.clear();
    wait = false;
    charge = false;
    cur = 0;
    cnt = 0;
  }

  void Run() {
    if(wait) {
      ++cost;
      //cout << "-";
      return;
    }
    //if(charge)
    //cout << ".";
    //    else
    //cout << "*";
    if(++cnt >= pat[cur]) {
      if(charge) {
	charging = 0;
      } else {
	cq.push_back(this);
	wait = true;
      }
      if(++cur >= (int)pat.size())
	cur = 0;
      cnt = 0;
      charge = !charge;
    }
  }
};

State st[100];

void Run() {
  if(charging == 0 && !cq.empty()) {
    charging = cq.front();
    cq.pop_front();
    charging->wait = false;
  }
  for(int i = 0; i < n; ++i)
    st[i].Run();
  //cout << endl;
}

int main() {
  while(cin >> n >> end_time && n) {
    for(int i = 0; i < n; ++i) {
      st[i].Init();
      int t;
      while(cin >> t && t)
	st[i].pat.push_back(t);
    }
    cost = 0;
    charging = 0;
    cq.clear();
    for(int i = 0; i < end_time; ++i) {
      Run();
    }
    cout << cost << endl;
  }
}