Bessie is hoping to fool Farmer John by building a herd of K realistic robotic cows (1 \leq K \leq 100,000).

It turns out that building a robotic cow is somewhat complicated. There are N (1 \leq n \leq 100,000) individual locations on the robot into which microcontrollers must be connected (so a single microcontroller must be connected at each location). For each of these locations, Bessie can select from a number of different models of microcontroller, each varying in cost.

For the herd of robotic cows to look convincing to Farmer John, no two robots should behave identically. Therefore, no two robots should have exactly the same set of microcontrollers. For any pair of robots, there should be at least one location at which the two robots use a different microcontroller model. It is guaranteed that there will always be enough different microcontroller models to satisfy this constraint.

Bessie wants to make her robotic herd as cheaply as possible. Help her determine the minimum possible cost to do this!

SAMPLE INPUT:

3 10
4 1 5 3 10
3 2 3 3
5 1 3 4 6 6

SAMPLE OUTPUT:

Problem credits: Richard Peng and Nathan Pinsker

#3988 upload 4 done 1 how_to_reg 1

Robotic Cow Herd timer 1s memory 128MB

#3988

Robotic Cow Herd 1s 128MB