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 cases 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

hide comments
SangKuan: 2015-10-27 10:38:37

Great problem

newbie: 2015-10-20 06:41:12

Got AC in 0.64.
TIP: GUYS BEWARE OF n=0.

robin_0: 2015-08-24 10:05:54

Wonderful Problem =D
Just Apply memorization DP :)

:.Mohib.:: 2015-06-27 22:08:14

Very Nice problem!!

kp: 2015-06-26 10:11:17

learnt a lot.. awesome problem

[Mayank Pratap]: 2015-06-12 06:16:50

Finally ....After many TLEs I got AC ... :)

Aditya Kumar: 2015-05-31 11:13:57

Think simple

kartikay singh: 2015-05-30 21:50:40

AC with 0.09s :)

Last edit: 2015-05-30 21:52:21
Madhav: 2015-03-24 11:07:31

A great problem...Many concepts involved....

sparrow: 2015-01-17 16:11:23

nice problem....

--edit(Francky)--> spoiler removed. Please read the notes below and apply them. Thanks in advance for the next time you'll propose a comment.

Last edit: 2015-01-17 16:12:38

Added by:gogo40
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