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**.### 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 -**x**,_{i}**y**and_{i}**c**denoting the_{i}**x**-coordinate,**y**-coordinate and the value of the**i**^{th}gem respectively.### 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**≤**10**^{5}**1**≤**c**≤_{i}**10**^{9}

### Subtasks

**Subtask #1 (15 points):****1**≤**N**≤**1000**,**1**≤**x**≤_{i}, y_{i}**2000****Subtask #2 (25 points):****1**≤**N**≤**10**,^{5}**1**≤**x**≤_{i}, y_{i}**2000****Subtask #3 (60 points):****1**≤**N**≤**10**,^{5}**1**≤**x**≤_{i}, y_{i}**10**^{5}

### 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.

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