#include <bits/stdc++.h>
using namespace std;

typedef long long ll;
typedef vector<int> vi;
typedef pair<ll,ll> pl;

#define f first
#define s second

int N,K;
ll tot; // sum of cheapest
vector<vi> v;

ll mx; ll res; int num;

void dfs(int pos, ll cur, int id) {
    if (cur > mx || num == K) return;
    res += cur; num ++;
    if (id+1 < v[pos].size())
        dfs(pos,cur+v[pos][id+1]-v[pos][id],id+1);
    for (int i = pos+1; i < v.size(); ++i) {
        ll CUR = cur+v[i][1];
        if (num == K || CUR > mx) break;
        dfs(i,CUR,1);
    }
}

void get() {
    res = num = 0;
    dfs(0,tot,0);
}

int main() {
    ios_base::sync_with_stdio(0); cin.tie(0);
    freopen("roboherd.in","r",stdin);
    freopen("roboherd.out","w",stdout);
    cin >> N >> K;
    for (int i = 0; i < N; ++i) {
        int m; cin >> m;
        vi p(m); for (int& x: p) cin >> x;
        sort(begin(p),end(p));
        tot += p[0]; for (int j = m-1; j >= 0; --j) p[j] -= p[0];
        if (p.size() > 1) v.push_back(p);
    }
    sort(begin(v),end(v)); // sort by second-cheapest
    ll lo = 0, hi = 1e13;
    while (lo < hi) {
        mx = (lo+hi+1)/2; get();
        if (num < K) lo = mx;
        else hi = mx-1;
    }
    mx = lo; get();
    cout << res+(K-num)*(mx+1) << "\n";
}