From Hero to Zero

1000ms

262144K

Description:

You are given an integer $$$n$$$ and an integer $$$k$$$.

In one step you can do one of the following moves:

decrease $$$n$$$ by $$$1$$$;
divide $$$n$$$ by $$$k$$$ if $$$n$$$ is divisible by $$$k$$$.

For example, if $$$n = 27$$$ and $$$k = 3$$$ you can do the following steps: $$$27 \rightarrow 26 \rightarrow 25 \rightarrow 24 \rightarrow 8 \rightarrow 7 \rightarrow 6 \rightarrow 2 \rightarrow 1 \rightarrow 0$$$.

You are asked to calculate the minimum number of steps to reach $$$0$$$ from $$$n$$$.

Input:

The first line contains one integer $$$t$$$ ($$$1 \le t \le 100$$$) — the number of queries.

The only line of each query contains two integers $$$n$$$ and $$$k$$$ ($$$1 \le n \le 10^{18}$$$, $$$2 \le k \le 10^{18}$$$).

Output:

For each query print the minimum number of steps to reach $$$0$$$ from $$$n$$$ in single line.

Sample Input:

2
59 3
1000000000000000000 10

Sample Output:

8
19

Note:

Steps for the first test case are: $$$59 \rightarrow 58 \rightarrow 57 \rightarrow 19 \rightarrow 18 \rightarrow 6 \rightarrow 2 \rightarrow 1 \rightarrow 0$$$.

In the second test case you have to divide $$$n$$$ by $$$k$$$ $$$18$$$ times and then decrease $$$n$$$ by $$$1$$$.

Informação

Provedor Codeforces

Código CF1175A