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.Scanner;

public class fromherotozero {
	public static void main(String[] args) {
		Scanner sc = new Scanner(System.in);
		int numQ = sc.nextInt();
		long[][] queries = new long[numQ][2];
		String t = sc.nextLine();
		for (int i = 0; i < numQ; i++) {
			queries[i][0] = sc.nextLong();
			queries[i][1] = sc.nextLong();
			t = sc.nextLine();
		}
		
		for (int i = 0; i < numQ; i++) {
			long a = queries[i][0];
			long b = queries[i][1];
			
			
			long numOps = 0;
			
			while (a != 0) {
				if (a % b == 0) {
					a = a/b;
					numOps++;
				}
				else {
					long numDivides = a / b;
					long total = b * numDivides;
					long diff = a - total;
					a = total;
					numOps += diff;
				}
			}
			System.out.println(numOps);
		}
	}
}



