A. k-rounding

For a given positive integer n denote its k-rounding as the minimum positive integer x, such that x ends with k or more zeros in base 10 and is divisible by n.

For example, 4-rounding of 375 is 375·80 = 30000. 30000 is the minimum integer such that it ends with 4 or more zeros and is divisible by 375.

Write a program that will perform the k-rounding of n.

Input

The only line contains two integers n and k (1 ≤ n ≤ 10⁹, 0 ≤ k ≤ 8).

Output

Print the k-rounding of n.

Examples

Input

375 4

Output

Input

10000 1

Output

Input

38101 0

Output

Input

123456789 8

Output

12345678900000000

每次考虑最后一位;

依次循环,

 1 #include <iostream>
 2 #define ll long long int
 3 using namespace std;
 4 int main(){
 5   int n,m;
 6   cin>>n>>m;
 7   ll t=n;
 8   for(int i=0;i<m;i++){
 9     if(n%10==0){
10       n=n/10;
11     }else if(n%5==0){
12       n=n/5;
13       t=t*2;
14     }else if(n%2==0){
15       n=n/2;
16       t=t*5;
17     }else{
18       t=t*10;
19     }
20   }
21   cout<<t<<endl;
22   return 0;
23 }