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.


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.


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



10 3

2 4 5



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

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

tle at test case 25:-(

rishab_arora89: 2017-02-21 21:04:57

Very Easy problem !! Just do Inclusion-exclusion !! :)

ganeshjadhav: 2016-12-27 06:55:18

read about bitmasking on codeforces

hacker_sk: 2016-10-02 12:10:58

lol, due to int .. i got 2 wrong ans in 25th(last) test case. finally AC. :)

karan_batra: 2016-09-13 10:06:17

AC in one go :D

Bhumit: 2016-09-05 10:53:40

@Paranoid Android
Can you please tell why I am getting NZEC in Java??
Submission ID - 17652754

[Mayank Pratap]: 2016-06-13 08:09:05

WA on 21 .. any help ??

kejriwal: 2016-02-01 17:05:54

AC in one go :) !!!
same algorithm in python giving NZEC/TLE/WA xP
@author can you tell me the glitch !

Last edit: 2016-02-02 17:50:24
GAURAV CHANDEL: 2016-01-20 16:51:34

Nice problem...

darkhire21: 2015-09-06 18:38:32

TLE in 25th test case

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