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
kira28: 2016-12-28 07:55:29

Modified sieve + Precomputation ...
TLE :( ->->-> AC :)

ani_geek9654: 2016-10-15 19:41:47

USed lower and upper bound stl and stored in Map.My 50th :)

sy_117: 2016-10-05 00:59:22

modified sieve + precomputation => AC in 0.18 sec

pt97: 2016-07-17 11:57:19

nice implementation of sieve and memorization :)

Deepak : 2016-07-06 20:52:55

finally AC : ) ....in .12.

ashiq_iqbal: 2016-04-03 19:37:16

modified sieve ... may be nothing else...

i_love_coding: 2016-03-12 21:21:08

SUCH A NICE PROBLEM...GET AC AFTER 5-6 attempts

proficient: 2016-03-05 16:47:59

AC in one go!!!

minhthai: 2016-02-05 13:25:15

such a nice problem! Be careful with your "limit" though :)

dwij28: 2016-01-06 06:57:55

Amazing ! If anyone ever asks me the list of best questions on SPOJ, this one is gonna rank very very high. Several TLE's before AC with 0.09 seconds. I applied memorization, 2D vectors, adapted sieve of eratosthenes, fast i-o, etc before finally realizing that my mistake was that i was iterating through all elements in (a, b) while using memorization. Used the std::upper_bound and std::lower_bound functions to finally get the green tick.


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