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.util.*;

public class Solution {
    static HashMap<Character, Integer> in;

    static boolean add(char a, char b, char c) {
        return (in.get(a) + in.get(b) + in.get(c)) == 7;
    }

    static public void main(String[] args) {
        Scanner sc = new Scanner(System.in);
        int s = sc.nextInt();
        while (s-- != 0) {
            long src = sc.nextLong();
            long d = sc.nextLong();
            long c = 0;
            while (src != 0) {
                long r = src % d;
                c += r;
                if ((src - r) == 0) {
                    break;
                }
                src = (src - r) / d;
                c++;
            }
            System.out.println(c);
        }
        sc.close();
    }
}