Beautiful results table#605
Oleg is a well-known enthusiast of programming competitions. He knows all participants from every competition over the past ten years and can tell, for any participant, how many problems the team with their participation solved at any contest. Additionally, Oleg loves number theory.
In the results table of a programming competition, teams are ordered by the number of problems they have solved in non-increasing order. Oleg calls the results table beautiful if, for every team, the number of problems they have solved is either zero or a divisor of the total number of problems in the contest. When a team submits a problem, the number of problems they have solved increases by one. No team can submit two or more problems at once, and no two teams can submit a problem at the same time.
Looking at a beautiful results table, Oleg wondered: how many more problems can the teams collectively submit, so that after each submission the table remains beautiful? Help him determine this number.
The first line of the input contains two integers: and — the number of teams and the number of problems in the contest, respectively (1 \leq n \leq 100, 1 \leq m \leq 10^9).
The second line contains integers in non-increasing order: for each team, the number of problems it has solved. It is guaranteed that all nonzero numbers are divisors of .
Output a single integer — the maximum number of problems that teams can still submit in total so that after each submission the results table remains beautiful.
Example 1