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. Lostborn

time limit per test

2 secondsmemory limit per test

256 megabytesinput

standard inputoutput

standard outputIgor K. very much likes a multiplayer role playing game WineAge II. Who knows, perhaps, that might be the reason for his poor performance at the university. As any person who plays the game, he is interested in equipping his hero with as good weapon and outfit as possible.

One day, as he was reading the game's forum yet again, he discovered a very interesting fact. As it turns out, each weapon in the game is characterised with *k* different numbers: *a*_{1}, ..., *a*_{k}. They are called hit indicators and according to the game developers' plan they are pairwise coprime.

The damage that is inflicted during a hit depends not only on the weapon's characteristics, but also on the hero's strength parameter. Thus, if the hero's strength equals *n*, than the inflicted damage will be calculated as the number of numbers on the segment , that aren't divisible by any hit indicator *a*_{i}.

Recently, having fulfilled another quest, Igor K. found a new Lostborn sword. He wants to know how much damage he will inflict upon his enemies if he uses it.

Input

The first line contains two integers: *n* and *k* (1 ≤ *n* ≤ 10^{13}, 1 ≤ *k* ≤ 100). They are the indicator of Igor K's hero's strength and the number of hit indicators.

The next line contains space-separated *k* integers *a*_{i} (1 ≤ *a*_{i} ≤ 1000). They are Lostborn sword's hit indicators. The given *k* numbers are pairwise coprime.

Output

Print the single number — the damage that will be inflicted by Igor K.'s hero when he uses his new weapon.

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

Examples

Input

20 3

2 3 5

Output

6

Input

50 2

15 8

Output

41

Codeforces (c) Copyright 2010-2020 Mike Mirzayanov

The only programming contests Web 2.0 platform

Server time: Jan/19/2020 03:57:03 (h3).

Desktop version, switch to mobile version.

Supported by

User lists

Name |
---|