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.
from decimal import Decimal
n = int(input())
datalist = []
ans = []
for _ in range(n):
    temp = input().split()
    datalist.append([int(temp[0]),int(temp[1])])

for item in datalist:
    n = item[0]
    k = item[1]
    ans.append(0)
    while n != 0: 
        ans[-1] += n%k+1
        n = int(Decimal(n)/Decimal(k))
        
        
        
for each in ans:
    print(each-1)
