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
tanav_shah1: 2019-11-05 21:13:39

Excellent question!!! Great use of sieve.

aayush_b1999: 2019-07-18 19:30:49

@rajat813 these are the 6 integers
30 42 60 66 70 78 84 90

rajat813: 2019-03-14 00:45:51

how answer of
1 100 3 is equal to 8

ameyanator: 2018-03-22 23:05:44

I've got a O(T+(X*root(X)) approach where X=10^6. Used preprocessing memoization. I've got an AC @1.18 secs but I see people with quite less runtimes ~<0.5secs. Whats the approach for it?

jh0n_12358: 2017-12-04 07:38:29

AC in one go

sas1905: 2017-06-16 21:47:54

Sieve + BIT ..:)

stranger77: 2017-05-28 03:05:13

AC in 0.06 sec .......use upper & lower bound stl.......

shahzada: 2017-03-01 08:44:22

Just Precomputation.

holmesherlock: 2017-01-24 16:35:36

tle at first but then precomputation came to rescue..:)

surajmall: 2017-01-24 15:17:58

NIce one simple at first look but indeed not :)


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