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>
#pragma GCC optimize("Ofast")
#pragma GCC target("avx,avx2,fma")
#pragma GCC optimization("unroll-loops")
using namespace std;
int main(void) {
  ios_base::sync_with_stdio(0);
  cin.tie(0);
  int n, k, siz, r;
  long long sum;
  cin >> n >> k;
  long long dp[n + 1][k + 1];
  memset(dp, 0, sizeof dp);
  for (int i = 1; i <= n; i++) {
    cin >> siz;
    for (int j = 1; j <= k; j++) {
      dp[i][j] = dp[i - 1][j];
    }
    sum = 0;
    for (int u = 1; u <= siz; u++) {
      cin >> r;
      sum += r;
      for (int j = u; j <= k; j++) {
        dp[i][j] = max(dp[i][j], dp[i - 1][j - u] + sum);
      }
    }
  }
  cout << dp[n][k];
}
