There are many ancient elemental monuments left on the continent of Teyvat. An elemental monument is a magical ancient mechanism, deeply rooted in the ground and unable to move.

Paimon is now solving a puzzle at some location. Here, there are elemental monuments arranged in a line. From left to right, the coordinate of the -th monument is , and each monument has one of two attributes: ice or fire.

If two monuments have different attributes, and the distance between them is strictly less than , then one piece of elemental particle will appear at their midpoint. A position may produce multiple pieces of elemental particles.

The puzzle requires collecting only the elemental particles that appear at integer coordinates, and the number of collected particles is the password to open the chest. Paimon asks you, the Traveler, for help. How many elemental particles will be collected in the end?

The first line contains two positive integers  (, ), representing the number of elemental monuments and the distance parameter (as described in the statement).

The second line contains  positive integers  (), representing the coordinates of the monuments.

The third line contains  integers  (), representing the attribute of each monument.  means fire, and  means ice.

Output one line containing an integer, representing the final number of elemental particles collected.

7 4
1 2 3 4 5 6 7
0 0 1 1 0 0 1

6