NGM2 - Another Game With Numbers


Little Chikoo likes to play with numbers. Often he plays the following game:

  1. He chooses a number N and a set of positive integers.
  2. He writes down all the numbers from 1 to N.
  3. He chooses the first number (say x) from the set and cancels out all the multiples of x from 1 to N, including x.
  4. He repeats step 3 for all the numbers from the set.

One day Little Chikoo was in a mood to play pranks. So his brother asked him to play the game with a certain challenge. He made the game a little harder and asked him to find out the number of integers which aren't cancelled after he completes step 4. If he does that then Little Chikoo gets to play on his brother's Nintendo for one full day. Now Little Chikoo is in a hurry and wants to finish the job as soon as possible. He has asked for your help.

Input

The first line of the input contains N and K. (N <= 10^9, K <= 15)

Then K numbers follow all in a single line. All numbers are <= 100.

Output

The output file must contain the number of integers that aren't cancelled after he finishes step 4 of the game.

Example

Input:
10 3
2 4 5

Output:
4

(The numbers 1, 3, 7 and 9 weren't cancelled).


hide comments
abhinav_jain02: 2019-05-23 17:23:03

@Alexander
if you are computing lcm indirectly using hcf,then don't do so.
it cost me wrong answer on test case 25.
just pre calculate lcm for all possible subsets.
Ensure that you always use long long.
You don't need double datatype anywhere.

Alexander: 2019-04-09 09:09:42

I have WA in 25+ test.
I use long long int. My program gives me the maximum possible answer (10^9) in one of my own tests.
I coded program with true iterator as explained in the problem and I generated number of quite different tests - all passed.
I pass for K=1, and even K=0, for K=15
I pass for N=1 and N=10^9, and even for N=0.
for different groups of Ks: prime numbers, including one, repeating, dividing each other, have common dividers.
WHAT. THE. HACK!
I hate when I stuck this way :)

linkret: 2019-03-31 15:04:30

no

fabijanb: 2019-03-31 14:06:59

where is segment tree in this problem? @linkret

linkret: 2019-03-27 16:43:03

such intrinsically good solution of this!

anirudnits: 2018-12-25 14:12:40

use long long int to clear the last test case!

Rahul Jain: 2018-07-19 15:36:29

Nintendo... no wonder question is from 2010 :D

abhi_upadhyay: 2017-12-28 13:25:38

use long long int, otherwise last test case will give wrong answer.

prodipdatta7: 2017-07-27 09:52:40

WA on test case 25!!!anyone help plz??

holmesherlock: 2017-03-26 16:35:45

tle at test case 25:-(


Added by:Paranoid Android
Date:2010-03-09
Time limit:0.247s
Source limit:50000B
Memory limit:1536MB
Cluster: Cube (Intel G860)
Languages:All except: NODEJS OBJC PERL6 VB.NET
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