A. Cutting back middle management

This is not the first crisis in the history of IGG. Whenever cost reduction was needed in the past, firing employees worked to some degree. This affected workers at the bottom of the food chain more often; managers could generally evade the threat. Over the decades this caused an unusually large amount of middle managers to accumulate. The CEO finally realized there's no other way to balance the structure of the company but to make their positions redundant.

A middle manager is somebody who has subordinates (who might also be managers), but the CEO is not a middle manager. Everyone can have at most M subordinates. If someone is fired, their subordinates are reassigned to their boss. Determine at most how many middle managers can be fired, such that the "at most M subordinates" rule still holds?

   target: suit & tie


First line contains N and M, where N is the number of managers. In the following N lines, the Ith line contains: It is guaranteed that the 0th manager is the CEO.


An integer: the amount of middle managers that can be fired.

Example input

10 4
0 3 6 2 3
2 1 9
2 1 8
2 1 1
4 0
1 0
0 2 7 4
4 0
1 1 5
1 0

Example output