codeforces 858A

A. k-rounding

time limit per test

1 second

memory limit per test

256 megabytes

input

standard input

output

standard output

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 10and 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

30000

input

10000 1

output

10000

input

38101 0

output

38101

input

123456789 8

output

12345678900000000

玩玩没想到啊 ，这题竟然是求10^k与n的最小公倍数。。。

可怜我想偏了，还wa了俩发才过T T。

附事后ac代码：

 1 #include <cstdio>
 2 #include <iostream>
 3 #include <cmath>
 4 #define ll long long
 5 ll gcd(ll a,ll b) {
 6     return a?gcd(b%a,a):b;
 7 }
 8 int main() {
 9     ll n,k;
10     scanf("%lld %lld",&n,&k);
11     k = pow(10,k);
12     printf("%lld\n",n*(k/gcd(k,n)));
13     return 0;
14
15
16 }