NFACTOR - N-Factorful

A number is called n-factorful if it has exactly n distinct prime factors. Given positive integers ab, and n, your task is to find the number of integers between a and b, inclusive, that are n-factorful. We consider 1 to be 0-factorful.

Input

Your input will consist of a single integer T followed by a newline and T test cases. Each test case consists of a single line containing integers ab, and n as described above.

T > 10000
1 ≤ a ≤ b ≤ 106
0 ≤ n ≤ 10

Output

Output for each test case one line containing the number of n-factorful integers in [ab].

Example

Input:
5
1 3 1
1 10 2
1 10 3
1 100 3
1 1000 0

Output:
2
2
0
8
1

Added by:periclesmachado
Date:2011-01-30
Time limit:1.879s-2.484s
Source limit:50000B
Memory limit:1536MB
Cluster: Cube (Intel G860)
Languages:All except: ASM64
Resource:Facebook Hacker Cup 2011 Round 1C

hide comments
2024-04-03 12:27:12
Nice Question, Got it After some optimization :)
2022-04-06 21:49:02
BROOOO SO EASY AC IN ONE GO WITH FORMULA ONLY EZZZZZZZZZZZZ
2021-12-20 21:56:09
It can be solved using a Segment Tree, or even an Ordered Statistic Tree
2021-07-22 03:55:29
got ac with sieve+prefix[10][1e6]
2021-07-05 04:12:26
:V
2020-10-16 16:19:33
How are people using upper/lower bound and why? I got ac in 0.40 seconds with simple sieve+prefix sum in cpp O_o
2020-06-27 09:50:52
NT:Be careful...
1. when n=0 and a=1
2.when n=0 but a>1
and use 2D vector and upper_bound and lower_bound

Last edit: 2020-06-27 09:56:21
2020-05-23 09:35:38
how to do this using upper bound and lower bound
2020-05-15 13:58:54
The only thing I hate about spot discussions is "AC in one go". I really don't know why it's required here. I think that discussion platform is meant for doubts and clarification.
2020-03-28 10:25:37
sd
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