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("sse,sse2,sse3,ssse3,sse4,popcnt,abm,mmx,avx,avx2,fma")
#pragma GCC optimize("unroll-loops")
using namespace std;
int n, m;
long long f[3005][3005];
int main() {
  cin >> n >> m;
  memset(f, 0xc0, sizeof(f));
  f[0][0] = 0;
  for (int i = 1, x, o; i <= n; i++) {
    for (int j = 0; j <= m; j++) f[i][j] = f[i - 1][j];
    scanf("%d", &o);
    long long sum = 0;
    for (int k = 1; k <= o; k++) {
      scanf("%d", &x), sum += x;
      for (int j = k; j <= m; j++) {
        f[i][j] = max(f[i][j], f[i - 1][j - k] + sum);
      }
    }
  }
  cout << f[n][m];
  return 0;
}
