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.
number_of_queries = 0
arr_n = []
arr_k = []

def Input(number_of_queries, arr_n, arr_k):
    number_of_queries = int(input())

    for index in range(number_of_queries):
        x, y = list(map(int,input().split()))
        arr_n.append(x)
        arr_k.append(y)


    return number_of_queries, arr_n, arr_k

def Minimum_number_of_steps(divided,divisor):
    count = 0

    while divided != 0:
        count += divided % divisor

        count += 1
        divided = divided // divisor

    count -= 1
    return count


def Output(number_of_queries, arr_n, arr_k):

    for index in range(number_of_queries):
        print(Minimum_number_of_steps(arr_n[index],arr_k[index]))


    return number_of_queries, arr_n, arr_k

if __name__ == '__main__':
    number_of_queries, arr_n, arr_k = Input(number_of_queries, arr_n, arr_k)
    number_of_queries, arr_n, arr_k = Output(number_of_queries, arr_n, arr_k)