ETFD - Euler Totient Function Depth


Lucky is fond of Number theory, one day he was solving a problem related to Euler Totient Function (phi) and found an interesting property of phi : phi(1) = 1, and for x > 1: phi(x) < x.
So if we define a sequence with a0 = x, and for n > 0: an = phi(an-1), this sequence will be constant equal to 1 starting from some point. Lets define depth(x) as minimal n such that an = 1. 
Now he is wondering how many numbers in a given range have depth equal to given number k. As you are a good programmer help Lucky with his task.

Input

Your input will consist of a single integer T  followed by a newline and T test cases.
Each test cases consists of a single line containing integers m, n, and k.

Output

Output for each test case one line containing the count of all numbers whose depth equals to k in given range [m, n].

Constraints

T < 10001
1 ≤ m ≤ n ≤ 10^6
0 ≤ k < 20

Example

Input:
5
1 3 1
1 10 2
1 10 3
1 100 3
1 1000000 17

Output:
1
3
5
8
287876

Explanation ::suppose number is 5 ; its depth will be 3. ( 5 -> 4 -> 2 -> 1 )

Note ::Depth for 1 is 0.


hide comments
besteady: 2016-09-06 15:11:35

@Lakshman - Hey, can you please check why I am getting WA ?

square1001: 2016-07-30 03:16:08

@Lakshman - This problem is good, but I think this problem is so similar to ProjectEuler 214.

Last edit: 2016-07-30 03:16:55
Ashutosh: 2016-07-08 23:41:38

Last edit: 2016-07-09 00:04:50
somya_v: 2016-03-26 14:36:27

@Lakshman can you please tell that which part in my code needs optimization...?
I am getting TLE

==(Lakshman)==> You are getting TLE on query part, Query part should be done in logarithmic time not in liner.

Last edit: 2016-05-03 08:57:35
[Lakshman]: 2015-11-28 02:51:29

@MuKeSh$ try to submit your own code don't cheat. I have disqualified your submission.

:.Mohib.:: 2015-10-22 23:31:06

Finally did It....!! Thanx @Lakshman for the great problem... :)

:.Mohib.:: 2015-07-16 16:55:04

@Lakshman can you please tell in my last submission, in which part I should optimize or in which part I am doing repeated calculations?? Thanks...

=(Lakshman)=>ETF part is okay. You need to answer each Query in Logarithmic time.

Last edit: 2015-07-17 05:17:07
:.Mohib.:: 2015-07-16 14:45:03

@Lakshman can you please check my code...I should optimize more or there is a specific algorithm to solve this que??

=(Lakshman)=> I just looked at your code, 1. You are computing same thing again and again. 2. You have to answer each Query in O(log n) time with some Pre-computation if Required. You have TLE in both Small and Large input files.

Last edit: 2015-07-16 14:56:55
deathgun: 2015-06-02 15:10:39

Nice Ques.. my 150th :D


Added by:[Lakshman]
Date:2015-01-14
Time limit:2s
Source limit:50000B
Memory limit:1536MB
Cluster: Cube (Intel G860)
Languages:All except: ASM64 JS-MONKEY
Resource:ETF