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CodeChef | Maximum Grid | August Challenge | Answer

There is an infinite grid given to you. Some of the cells in this infinite grid have gems in them. Each gem a parameter beauty associated with it which is given by a positive integer.
You will be given an integer L. You have to find maximum sum of beauties inside any square sub-grid with its side length being less than or equal to L. Let S be that number, i.e. the maximum sum of beauties for some sub-grid with side length no greater than L. You also have to find minimum side length such that there exists some sqaure sub-grid with that given side length with sum of beauties of gems inside it being equal toS.

Input

First line of the input contains two space separated N and L, denoting the number of gems and the maximum allowed size of the sub-grid, respectively.
Each of the next N lines contains three space separated integers - xiyi and ci denoting the x-coordinate, y-coordinate and the value of the ith gem respectively.


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Output

Output a single line containing two space separated integers: the maximum value of the sum of beauties of gem in some square sub-grid of the length not greater than L and the minimum side length of the square-grid which contains that much sum of beauties of gems inside it, respectively.

Constraints

  • 1 ≤ L ≤ 105
  • 1 ≤ ci ≤ 109

Subtasks

  • Subtask #1 (15 points): 1 ≤ N ≤ 10001 ≤ xi, yi ≤ 2000
  • Subtask #2 (25 points): 1 ≤ N ≤ 1051 ≤ xi, yi ≤ 2000
  • Subtask #3 (60 points): 1 ≤ N ≤ 1051 ≤ xi, yi ≤ 105

Example

Input:
3 2
1 1 1
2 1 1
3 1 5

Output:
6 2

Explanation

In the given example, you can create a 2X2 sub-grid with top-left corner as (2,1) and bottom right corner as (3,2) with value 6. All other sub-grids have value lower than or equal to this sub-grid.


                                        ANSwER