Sum

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

inputFormat

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.

outputFormat

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

样例

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

26

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