For a positive, non-zero integer N, find the minimum count of numbers of the form X^(i-1), where X is a given non-zero, non-negative integer raised to the power i-1 (1<=i<=12), so that they sum up to form the number N exactly.

**Input:**

First line of input is an integer T denoting the number of test cases. For each test case, there are further two lines of input. First line comprises the integer N and second line comprises the integer X, for which any value of i can be taken in its power to satisfy the condition.

**Output:**

The only line of output is the minimum number of values of X^(i-1), with any value of i in the range 1 to 12, which sum up to the number N exactly. If a particular value of X^(i-1) is taken up two or more times, the count considered will be two or more respectively.

**Constraints:**

1<=T<=100

2<=X<=5

1<=N<10^8

**Example:**

**Input:**

4

10

2

38

3

1005

5

99999999

4

**Output:**

2

4

5

45

**Explanation:**

In the first test case, N=10 and X=2, which means the sum of 10 has to be made out of possible values of 2^(i-1).

1+1+1+1+1+1+1+1+1+1=10 , count is 10 here. (1=2^(1-1))

1+1+1+1+1+1+1+1+2=10 , count is 9 here. (2=2^(2-1))

1+1+1+1+1+1+4=10, count is 7 here. (4=2^(3-1))

1+1+8=10, count here is 3. (8=2^(4-1))

2+8=10, count is 2 here, which is minimum of all. Therefore, the output is 2. Similarly, all other results are to be found.

Data type int will be insufficient to store a value as large as 99999999, therefore you can use long int or long long int instead.

If you have purchased any course from GeeksforGeeks then please ask your doubt on course discussion forum. You will get quick replies from GFG Moderators there.

preparecodinginterview_dot_com | 190 |

__murugan__ | 173 |

xiaoyan_yunche | 168 |

manvimahajan20 | 140 |

manvirag982 | 124 |

preparecodinginterview_dot_com | 190 |

__murugan__ | 173 |

xiaoyan_yunche | 168 |

arpit_anshuman | 168 |

manvimahajan20 | 166 |

blackshadows | 5331 |

Ibrahim Nash | 5219 |

akhayrutdinov | 5111 |

mb1973 | 4929 |

Quandray | 4567 |

Login to report an issue on this page.