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 → 26 → 25 → 24 → 8 → 7 → 6 → 2 → 1 → 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 ≤ t ≤ 100) — the number of queries.

The only line of each query contains two integers n and k (1 ≤ n ≤ 10^{18}, 2 ≤ k ≤ 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 → 58 → 57 → 19 → 18 → 6 → 2 → 1 → 0.

In the second test case you have to divide n by k 18 times and then decrease n by 1.
import java.io.PrintWriter;
import java.util.Scanner;

public class PathToNull {
    public static void main(String[] args) {
        final Scanner sc = new Scanner(System.in);
        final PrintWriter pw = new PrintWriter(System.out);

        int t = sc.nextInt();

        for (int i = 0; i < t; ++i) {
            long n = sc.nextLong();
            long k = sc.nextLong();

            long answer = 1;

            while (n != 1) {
                if (k > n) {
                    answer += (n - 1);
                    break;
                } else if (n % k == 0) {
                    n /= k;
                    ++answer;
                } else if (n > k) {
                    long temp = n / k * k;
                    answer += (n - temp);
                    n = temp;
                }
            }

            pw.println(answer);

        }

        pw.flush();
    }
}