Popcorn

We all know that popcorn is a culinary delicacy. While you were preparing for this year's selection camp (and the after parties), you ordered $N$ types of microwave popcorn. For each different type you know $3$ values:

• $A\_i$ ​= the time (in seconds) when the popcorn of type $i$ pops
• $B\_i$ ​= the time (in seconds) then the popcorn of type $i$ gets burned
• $C\_i$ ​= the quantity of popcorn of type $i$

You also have $M$ disposable popcorn bags of large capacity (practically, infinite) and a microwave oven. As, of course, no one likes burned or unpopped popcorn, you wish to partition it in the $M$ bags and then put those in the oven, setting a certain cooking time $prep\_i$, such that in the end you'll have as much edible popcorn as possible.

Formally, the popcorn of type $i$ used in bag $j$, which was cooked in the oven $prep\_j$ seconds, is edible if and only if $A\_i≤prep\_j\<B\_i$.

Given $N$ types of popcorn and the number of available bags, you have to find a convenient partition and the cooking times for each bag, such that in the end you'll have as much edible popcorn as possible. Output the quantity of edible popcorn. Too simple!

The first line contains two integers $N$ and $M$.

Each of the next $N$ lines contains $3$ integers $A\_i$, $B\_i$, $C\_i$, corresponding to each popcorn type.

Output a single integer representing the maximum quantity of edible popcorn you can get.

• $1≤M≤N≤200\\, 000$
• $1≤A\_i≤B\_i≤200\\, 000$
• The total quantity of popcorn doesn't exceed $10^9$
• Some bags can be left empty!
• Let $X=\max\\{N,B\[1],B\[2],\dots ,B\[N]\\}$