There are n piles of coins on a table. Each pile consists of a positive number of coins of assorted denominations.

In one move, you can choose any coin on top of any pile, remove it, and add it to your wallet.

Given a list piles, where piles[i] is a list of integers denoting the composition of the i^(th) pile from top to bottom, and a positive integer k, return the maximum total value of coins you can have in your wallet if you choose exactly k coins optimally.

Examples

Example 1

Input:  piles = [[1,100,3],[7,8,9]], k = 2
Output: 101

The above diagram shows the different ways we can choose k coins. The maximum total we can obtain is 101.

Example 2

Input:  piles = [[100],[100],[100],[100],[100],[100],[1,1,1,1,1,1,700]], k = 7
Output: 706

The maximum total can be obtained if we choose all coins from the last pile.

Constraints

• n == piles.length
• 1 <= n <= 1000
• 1 <= piles[i][j] <= 10⁵
• 1 <= k <= sum(piles[i].length) <= 2000