ETFS - Euler Totient Function Sieve


Leonhard Euler Totient

In number theory, the totient phi(n) of a positive integer n is defined to be the number of positive integers less than or equal to n that are coprime to n.

Input

The lonely line in input contains two integers a, b.

Output

Print phi(n) for n from a to b (inclusive).

Example

Input:
1 5

Output:
1
1
2
2
4

Constraints

0 < a < b < 10^14
b - a < 10^5

Python can get AC under half the time limit (for any test case). My total PY3.4 time is 3.23s for 5 input files.
Have fun ;-)


hide comments
vikas12: 2020-04-17 23:03:54

i am also gettin wa for4 th testcase
please help to resolve

rjsingh_123: 2020-04-14 17:55:10

Getting wrong answer on case 4
Tried multiple times
@Francky can you please help on submission 25765715
A small hint would be really helpful :)

=(Francky)=> It seems you figured it out by yourself ; well done.

Last edit: 2020-04-15 10:25:03
az_09_18je0028: 2020-04-13 15:50:59

Last edit: 2020-10-08 13:44:23
sanjiuchiha: 2020-04-13 15:10:19

I am getting wrong answer on test case 4. I have checked my code multiple times. Can somebody give me a hint.
@Francky ,can you please check my submission 25757062. I have generated primes and then used ETF sieve.
Please help me.

=(Francky)=> You have WA for big inputs. You could check that with any brute force method and a small range. Good luck.

Last edit: 2020-04-13 16:35:26
i_0__0_i: 2020-04-11 10:41:45

99999999899998 99999999999999 -isn't this is a valid test case?
but when i use it it takes forever to run!!

=(Francky)=> It's a valid test case, you're about to solve it fast. Good luck.

Last edit: 2020-04-11 23:33:16
zihadboss: 2020-03-22 23:22:58

Give me hint to solve the problem.
=(Francky)=> Build a sieve specific for totient function.

Last edit: 2020-03-23 18:51:19
ashik_01: 2019-08-08 19:52:13

Just a superb problem. Learned something new. Thanks to the author.

abhinav_jain02: 2018-12-19 13:33:51

I am getting wrong answer on test case 4. I have checked my code multiple times. Can somebody give me a hint.
@Francky ,can you please check my submission 22907703. I have generated primes and then used ETF sieve.
Please help me.
Thank you very much,Francky
Finally found my mistake and got my solution accepted

=(Francky)=> You have some negative outputs for big inputs. Are you sure you well tested you code against brute force totient (no sieve) ?

Last edit: 2019-05-16 16:04:24
eagleshadow: 2018-10-03 16:23:00

Very nice Problem
if you are getting wrong answer just look for the value of phi(10) , ans see if it is 4 or not
you will find the mistake :)

jmr99: 2018-08-16 16:55:46

nice problem!

Last edit: 2018-08-16 21:43:53

Added by:Francky
Date:2014-12-29
Time limit:2s
Source limit:50000B
Memory limit:1536MB
Cluster: Cube (Intel G860)
Languages:All except: ASM64
Resource:ETF