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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 to S.
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 - xi, yi and ci denoting the x-coordinate, y-coordinate and the value of the ith gem respectively.
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.
- 1 ≤ L ≤ 105
- 1 ≤ ci ≤ 109
- Subtask #1 (15 points): 1 ≤ N ≤ 1000, 1 ≤ xi, yi ≤ 2000
- Subtask #2 (25 points): 1 ≤ N ≤ 105, 1 ≤ xi, yi ≤ 2000
- Subtask #3 (60 points): 1 ≤ N ≤ 105, 1 ≤ xi, yi ≤ 105
Input: 3 2 1 1 1 2 1 1 3 1 5 Output: 6 2
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.
|Tags||aug16, kevind, medium, segment-tree, sweepline|
|Time Limit:||5 sec|
|Source Limit:||50000 Bytes|
|Languages:||C, CPP14, JAVA, PYTH, PYTH 3.6, PYPY, CS2, PAS fpc, PAS gpc, RUBY, PHP, GO, NODEJS, HASK, SCALA, D, PERL, FORT, WSPC, ADA, CAML, ICK, BF, ASM, CLPS, PRLG, ICON, SCM qobi, PIKE, ST, NICE, LUA, BASH, NEM, LISP sbcl, LISP clisp, SCM guile, JS, ERL, TCL, PERL6, TEXT, SCM chicken, CLOJ, FS|
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