## KDIV - K-Divisors

The

If we define the positive divisor function as

Calculating

*positive divisor function*is defined as a function that counts the number of positive divisors of an integer**N**, including**1**and**N**.If we define the positive divisor function as

**D(N)**, then, for example:**D(1) = 1****D(2) = 2****D(10) = 4****D(24) = 8**Calculating

**D(N)**is a classical problem and there are many efficient algorithms for that. But what if you are asked to find something different? Given a range and an integer**K**, can you find out for how many**N**in the given range,**D(N)**equals**K**?### Input

In the very first line, youâ€™ll have an integer called**T**. This is the number of test cases that shall follow. Every test case contains three integers,**L**,**R**, and**K**.**L**and**R**represent the range and are inclusive.### Constraints

**1 ≤ T < 31**

**1 ≤ L ≤ R < 2**

^{31}1 ≤ K < 2 ^{31}

### Output

For every test case, you must print the case number, followed by the count of numbers with exactly**K**divisors in the range.### Sample Input

3 10 10 4 2 13 2 100 10000 100

### Sample Output

Case 1: 1 Case 2: 6 Case 3: 0

Added by: | sgtlaugh |

Date: | 2020-02-22 |

Time limit: | 3s |

Source limit: | 50000B |

Memory limit: | 1536MB |

Cluster: | Cube (Intel G860) |

Languages: | All |

Resource: | Own Problem |