# USACO 2016 December Contest, Platinum Problem 3. Robotic Cow Herd

USACO2016DEC-G3

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

using namespace std;

int N, M;
vector<int> A[100010];
int F[100010];
int totalcount;
long long savings;

void search(int x, long long budget) {
if (totalcount >= M) {
return;
}
if (x != -1 && budget < A[x][0]) {
x = upper_bound(F, F + x, (int)budget) - F - 1;
}
if (x == -1) {
totalcount++;
return;
}
search(x - 1, budget);
for (int i = 0; i < A[x].size() && A[x][i] <= budget; i++) {
search(x - 1, budget - A[x][i]);
}
}

void enumerate(int x, long long budget) {
if (x != -1 && budget < A[x][0]) {
x = upper_bound(F, F + x, (int)budget) - F - 1;
}
if (x == -1) {
savings += budget + 1;
return;
}
enumerate(x - 1, budget);
for (int i = 0; i < A[x].size() && A[x][i] <= budget; i++) {
enumerate(x - 1, budget - A[x][i]);
}
}

int main() {
cin >> N >> M;

long long base = 0;
long long mx = 0;
for (int i = 0; i < N; i++) {
int sz; cin >> sz;

vector<int> V(sz);
for (int j = 0; j < sz; j++) {
cin >> V[j];
}
sort(V.begin(), V.end());

base += V[0];
if (sz == 1) {
i--;
N--;
continue;
}
for (int j = 1; j < sz; j++) {
A[i].push_back(V[j] - V[0]);
}
mx += A[i].back();
}

sort(A, A + N);
for (int i = 0; i < N; i++) {
F[i] = A[i][0];
}

long long lo = 0;
long long hi = mx;
while (lo < hi) {
long long md = (lo + hi) / 2;
totalcount = 0;
search(N - 1, md);
if (totalcount < M) {
lo = md + 1;
} else {
hi = md;
}
}

savings = 0;
if (lo > 0) {
enumerate(N - 1, lo - 1);
}
cout << (base + lo) * M - savings << endl;

return 0;
}