You are given n non-decreasing arrays of non-negative numbers. 

Vasya repeats the following operation k times: 

  * Selects a non-empty array. 
  * Puts the first element of the selected array in his pocket. 
  * Removes the first element from the selected array. 



Vasya wants to maximize the sum of the elements in his pocket.

Input

The first line contains two integers n and k (1 ≤ n, k ≤ 3 000): the number of arrays and operations.

Each of the next n lines contain an array. The first integer in each line is t_i (1 ≤ t_i ≤ 10^6): the size of the i-th array. The following t_i integers a_{i, j} (0 ≤ a_{i, 1} ≤ … ≤ a_{i, t_i} ≤ 10^8) are the elements of the i-th array.

It is guaranteed that k ≤ ∑_{i=1}^n t_i ≤ 10^6.

Output

Print one integer: the maximum possible sum of all elements in Vasya's pocket after k operations.

Example

Input


3 3
2 5 10
3 1 2 3
2 1 20


Output


26
#include <bits/stdc++.h>
using namespace std;
int read() {
  char ch = '!';
  int res = 0, f = 0;
  while (!isdigit(ch)) {
    ch = getchar();
    if (ch == '-') f = 1;
  }
  while (isdigit(ch)) res = res * 10 + ch - '0', ch = getchar();
  return f ? -res : res;
}
const int N = 3003;
int n, K, t[N], top;
vector<int> arr[N];
long long f[N], tf[N], sum[N], stk[30][N], ans;
void push(long long *p) {
  ++top;
  for (int i = 0; i <= K; ++i) stk[top][i] = p[i], f[i] = p[i];
}
void pop() {
  --top;
  for (int i = 0; i <= K; ++i) f[i] = stk[top][i];
}
void divide(int l, int r) {
  if (l == r) {
    long long now = 0;
    for (int i = 0; i <= t[l] && i <= K; ++i)
      now += arr[l][i], ans = max(ans, now + f[K - i]);
    return;
  }
  int mid = (l + r) >> 1;
  memcpy(tf, f, sizeof(long long) * (K + 1));
  for (int i = mid + 1; i <= r; ++i)
    for (int j = K; j >= t[i]; --j) tf[j] = max(tf[j - t[i]] + sum[i], tf[j]);
  push(tf), divide(l, mid), pop();
  memcpy(tf, f, sizeof(long long) * (K + 1));
  for (int i = l; i <= mid; ++i)
    for (int j = K; j >= t[i]; --j) tf[j] = max(tf[j - t[i]] + sum[i], tf[j]);
  push(tf), divide(mid + 1, r), pop();
}
int main() {
  n = read(), K = read();
  for (int i = 1; i <= n; ++i) {
    t[i] = read(), arr[i].resize(t[i] + 1);
    for (int j = 1; j <= t[i]; ++j) arr[i][j] = read(), sum[i] += arr[i][j];
  }
  divide(1, n);
  cout << ans;
  return 0;
}
