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 FromZeroToHero {
	public static void main(String[] args) {
		Scanner in = new Scanner(System.in);
		int cases = Integer.parseInt(in.nextLine());
		long[] res = new long[cases];

		for(int c = 0; c < cases; c++) {
			String[] nums = in.nextLine().split(" ");
			res[c] = calc(Long.parseLong(nums[0]), Long.parseLong(nums[1]));
		}

		for(long r : res) {
			System.out.println(r);
		}
	}

	public static long calc(long n, long k) {
		if(n < k) return n;
		else if(n%k == 0) return 1 + calc(n/k, k);
		else return 1 + (n%k) + calc(n/k, k);
	}
}