City of Lights#9686
Paris has been called "ville lumière" (city of lights) since the 17th century. It earned this nickname in part because of the many city lights illuminating famous sites such as monuments, statues, churches, or fountains.
Those public lights in Paris are numbered from to and are all on by default. A group of hackers has gained the capability to toggle groups of lights. Every time the hackers use their program, they cause a number (that they cannot control) to be sent to the system controlling the city lights. The lights numbered i, 2i, 3i and so on (up to ) then change state instantly: lights that were on go off, and lights that were off go on.
During the night, the hackers use their programs times. What is the greatest number of lights that are simultaneously off at the same time?
Consists of several lines, each consisting of a single integer:
The first line contains the number n~(1 \le n \le 10^6) of lights.
The second line contains the number k~(1 \le k \le 100) of uses of the hacker program.
The next lines contain a number i~(1 \le i \le n) sent to the system controlling the lights.
Print one integer, the greatest number of lights that are simultaneously off at the same time.
Example 1