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;
long long int ans;
void update(int l, int r, long long int *dp, int k, long long int **a, int *w) {
  if (l == r) {
    for (int i = 0; i <= k; ++i) {
      ans = max(ans, dp[i] + a[l][min(w[l], k - i)]);
    }
  } else {
    int mid = (l + r) >> 1;
    long long int *dptemp = new long long int[k + 1];
    for (int i = 0; i <= k; ++i) dptemp[i] = dp[i];
    for (int i = mid + 1; i <= r; ++i) {
      for (int j = k; j >= w[i]; --j)
        if (dptemp[j - w[i]] >= 0)
          dptemp[j] = max(dptemp[j], dptemp[j - w[i]] + a[i][w[i]]);
    }
    update(l, mid, dptemp, k, a, w);
    for (int i = 0; i <= k; ++i) dptemp[i] = dp[i];
    for (int i = l; i <= mid; ++i) {
      for (int j = k; j >= w[i]; --j)
        if (dptemp[j - w[i]] >= 0)
          dptemp[j] = max(dptemp[j], dptemp[j - w[i]] + a[i][w[i]]);
    }
    update(mid + 1, r, dptemp, k, a, w);
  }
}
int main() {
  ios_base::sync_with_stdio(false);
  cin.tie(NULL);
  cout.tie(NULL);
  int n, k;
  cin >> n >> k;
  long long int **a = new long long int *[n];
  int *w = new int[n];
  for (int i = 0; i < n; ++i) {
    cin >> w[i];
    a[i] = new long long int[w[i] + 1];
    a[i][0] = 0;
    for (int j = 1; j <= w[i]; ++j) {
      cin >> a[i][j];
      a[i][j] += a[i][j - 1];
    }
  }
  long long int *dp = new long long int[k + 1];
  dp[0] = 0;
  for (int i = 1; i <= k; ++i) dp[i] = -1;
  update(0, n - 1, dp, k, a, w);
  cout << ans;
}
