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 Hero to Zero ###
### https://codeforces.com/contest/1175/problem/A ###
t=int(input())
kq=[]
for i in range(0,t):
    kq.append(0)
    nk=input()
    nk=nk.split()
    nk[1]=eval(nk[1])
    nk[0]=eval(nk[0])
    while nk[0]!=0:
        if nk[0] % nk[1]==0:
            nk[0] = nk[0] // nk[1]
            kq[i] = kq[i] + 1
        else:
            a = nk[0] % nk[1]
            nk[0] = nk[0] - a
            kq[i] = kq[i] + a
for i in range(0,t):
    print(round(kq[i],0))
