Package for this problem was not updated by the problem writer or Codeforces administration after we’ve upgraded the judging servers. To adjust the time limit constraint, solution execution time will be multiplied by 2. For example, if your solution works for 400 ms on judging servers, then value 800 ms will be displayed and used to determine the verdict.

Virtual contest is a way to take part in past contest, as close as possible to participation on time. It is supported only ICPC mode for virtual contests.
If you've seen these problems, a virtual contest is not for you - solve these problems in the archive.
If you just want to solve some problem from a contest, a virtual contest is not for you - solve this problem in the archive.
Never use someone else's code, read the tutorials or communicate with other person during a virtual contest.

No tag edit access

E. Three Horses

time limit per test

2 secondsmemory limit per test

256 megabytesinput

standard inputoutput

standard outputThere are three horses living in a horse land: one gray, one white and one gray-and-white. The horses are really amusing animals, which is why they adore special cards. Each of those cards must contain two integers, the first one on top, the second one in the bottom of the card. Let's denote a card with *a* on the top and *b* in the bottom as (*a*, *b*).

Each of the three horses can paint the special cards. If you show an (*a*, *b*) card to the gray horse, then the horse can paint a new (*a* + 1, *b* + 1) card. If you show an (*a*, *b*) card, such that *a* and *b* are even integers, to the white horse, then the horse can paint a new card. If you show two cards (*a*, *b*) and (*b*, *c*) to the gray-and-white horse, then he can paint a new (*a*, *c*) card.

Polycarpus really wants to get *n* special cards (1, *a*_{1}), (1, *a*_{2}), ..., (1, *a*_{n}). For that he is going to the horse land. He can take exactly one (*x*, *y*) card to the horse land, such that 1 ≤ *x* < *y* ≤ *m*. How many ways are there to choose the card so that he can perform some actions in the horse land and get the required cards?

Polycarpus can get cards from the horses only as a result of the actions that are described above. Polycarpus is allowed to get additional cards besides the cards that he requires.

Input

The first line contains two integers *n*, *m* (1 ≤ *n* ≤ 10^{5}, 2 ≤ *m* ≤ 10^{9}). The second line contains the sequence of integers *a*_{1}, *a*_{2}, ..., *a*_{n} (2 ≤ *a*_{i} ≤ 10^{9}). Note, that the numbers in the sequence can coincide.

The numbers in the lines are separated by single spaces.

Output

Print a single integer — the answer to the problem.

Please, do not use the %lld specifier to read or write 64-bit integers in C++. It is preferred to use the cin, cout streams or the %I64d specifier.

Examples

Input

1 6

2

Output

11

Input

1 6

7

Output

14

Input

2 10

13 7

Output

36

Codeforces (c) Copyright 2010-2020 Mike Mirzayanov

The only programming contests Web 2.0 platform

Server time: Sep/21/2020 07:29:04 (h2).

Desktop version, switch to mobile version.

Supported by

User lists

Name |
---|