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A. From Hero to Zero

time limit per test

1 secondmemory limit per test

256 megabytesinput

standard inputoutput

standard outputYou 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.

Example

Input

2 59 3 1000000000000000000 10

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 $$$1$$$.

Codeforces (c) Copyright 2010-2021 Mike Mirzayanov

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