PRSQRFR  Perfect Composites
Rohil and Mahesh recently attended a class on Prime Numbers. They learnt about a term "Prime Score" which is defined for all N > 1. For a number N = p1^{a} x p2^{b} x p3^{b} ... x pk^{m} where p1,p2,...pk are prime factors of N, Prime Score of N = a+b+...+m. While Mahesh was interested only in primes, Rohil thought how about playing around with Composite Numbers. Both started discussing and found out something known as Perfect Composite Numbers. They defined a Composite number N as Perfect Composite if it is divisible by all the factors of its Prime Score.
Whoa!! That's a nice discovery both of them have made. Now, they are interested in finding the number of Perfect Composites between A and B (inclusive) having Prime Score K. They want you to write a program for the same.
INPUT SPECIFICATIONS
First line contains a single integer T <= 10000, the number of testcases. Each following line contains three integers A, B and K (2 <= A <= B <= 10^{5} and K >= 0).
OUTPUT SPECIFICATIONS
For each test case, print a single integer  the number of Perfect Composite numbers between A and B (inclusive) having Prime Score = K.
SAMPLE I/O
INPUT :
5
2 5 2
3 100 3
4 10 5
90 456 8
34 67 5
OUTPUT :
1
11
0
2
0
hide comments
prodipdatta7:
20191015 13:25:19
what do you mean by 'factor' ? Is it divisor or the prime factor of the score k ? 

nadstratosfer:
20180418 13:10:25
How the hell did others get AC following statement like this? Perfect composite is divisible by its prime score, not just the "factors" of it. Eg. 100 is a PC with score 4 but 90 is not. AC'd with a desperate guess :/

Added by:  Mahesh Chandra Sharma 
Date:  20110128 
Time limit:  1s 
Source limit:  50000B 
Memory limit:  1536MB 
Cluster:  Cube (Intel G860) 
Languages:  All except: ASM64 
Resource:  Own Problem 