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
Radhakrishnan Venkataramani: 2011-01-31 15:53:17

Nice Modification to the Original problem :)
But i didn see any problem with T>10000 instead of T<10000

Last edit: 2011-01-31 15:53:59

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