FCDC - Factorial Modulo

You are given 2 integers a, b. Find the number of i for which i! is divisible by a but not b. if i! is divisible by a and b, then you should not count that i.

Input

One line that contains a and b.

Output

Output the result in one line.

Example

Input:
2 3

Output:
1

Constraints

1 ≤ a ≤ b ≤ 107

Explanation

2! is the only factorial which is divisible by 2 and not divisible by 3.


Added by:Ruhan Habib
Date:2015-11-05
Time limit:1s
Source limit:50000B
Memory limit:1536MB
Cluster: Cube (Intel G860)
Languages:All except: ASM64 GOSU JS-MONKEY
Resource:Own Problem

hide comments
2021-09-27 03:55:30
your answer should not be negative
2021-06-26 11:23:40
Factorization + Binary search
Loved the problem :D
2019-02-09 16:40:31 tanardi gunawan
good problem
2018-11-22 16:29:22
nice problem..enjoyed solving it.Thanks Ruhan!
2018-08-20 09:10:30
did it using binary search and highest power of a prime in n!. Enjoyed the problem. Hope it helps someone in need. All the best!!!
2018-07-01 17:06:34
AC in 10 min :)


Last edit: 2018-07-01 17:07:43
2018-05-26 11:46:44
Factorization and brain storming :)
2018-05-18 22:43:37
that's a easy one :)
factorization+simple logic
2017-10-24 16:53:15
dont think too much,,simple logic will get you through
2017-10-20 06:04:48
Seemed easy but took me good 2 hours to crack. The implementation is not so straightforward either - my code came out quite bloated - but considering half of C submissions are slower than my Python3 one, you can probably bruteforce in a few lines also.
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