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.
def Input(T, n, k):
    T = int(input())
    for i in range(T):
        tmpn, tmpk = list(map(int,input().split()))
        n.append(tmpn)
        k.append(tmpk)
    return T, n, k
def Processing(T, n, k):
    for i in range(T):

        result = int(0)
        x = int(n[i])
        y = int(k[i])
        while x != 0:
            if x < y:
                result += x
                break
            if x % y == 0:
                result += 1
                x = x // y
                continue
            tmp = int((x // y) * y)
            result += int(x - tmp + 1)
            x = int(tmp)
            x = x // y
        print(int(result), end = '\n')
if __name__ == "__main__":
    n = []
    k = []
    T = 0
    T, n, k = Input(T, n, k)
    Processing(T, n, k)