One day a highly important task was commissioned to Vasya — writing a program in a night. The program consists of n lines of code. Vasya is already exhausted, so he works like that: first he writes v lines of code, drinks a cup of tea, then he writes as much as lines, drinks another cup of tea, then he writes
lines and so on:
,
,
, ...
The expression is regarded as the integral part from dividing number a by number b.
The moment the current value equals 0, Vasya immediately falls asleep and he wakes up only in the morning, when the program should already be finished.
Vasya is wondering, what minimum allowable value v can take to let him write not less than n lines of code before he falls asleep.
Input
The input consists of two integers n and k, separated by spaces — the size of the program in lines and the productivity reduction coefficient, 1 ≤ n ≤ 109, 2 ≤ k ≤ 10.
Output
Print the only integer — the minimum value of v that lets Vasya write the program in one night.
Example
7 2
4
59 9
54
Note
In the first sample the answer is v = 4. Vasya writes the code in the following portions: first 4 lines, then 2, then 1, and then Vasya falls asleep. Thus, he manages to write 4 + 2 + 1 = 7 lines in a night and complete the task.
In the second sample the answer is v = 54. Vasya writes the code in the following portions: 54, 6. The total sum is 54 + 6 = 60, that's even more than n = 59.
1 #include<iostream> 2 #include<algorithm> 3 #include<cstdio> 4 using namespace std; 5 6 int n,k; 7 8 bool check(int ans) 9 { int sum=0; 10 while(ans!=0){ 11 sum+=ans; 12 ans/=k; 13 } 14 if(sum>=n) return true; 15 else return false; 16 } 17 int main() 18 { cin>>n>>k; 19 int l=1,r=n; 20 int mid; 21 while(l<r){ 22 mid=(l+r)/2; 23 if(check(mid)) r=mid; 24 else l=mid; 25 if(r-l==1) break; 26 } 27 if(check(l)) printf("%d ",l); 28 else printf("%d ",r); 29 }