CodeForces758D

D. Ability To Convert

time limit per test:1 second

memory limit per test:256 megabytes

input:standard input

output:standard output

Alexander is learning how to convert numbers from the decimal system to any other, however, he doesn't know English letters, so he writes any number only as a decimal number, it means that instead of the letter A he will write the number 10. Thus, by converting the number 475 from decimal to hexadecimal system, he gets 11311 (475 = 1·162 + 13·161 + 11·160). Alexander lived calmly until he tried to convert the number back to the decimal number system.

Alexander remembers that he worked with little numbers so he asks to find the minimum decimal number so that by converting it to the system with the base n he will get the number k.

Input

The first line contains the integer n (2 ≤ n ≤ 109). The second line contains the integer k (0 ≤ k < 1060), it is guaranteed that the number kcontains no more than 60 symbols. All digits in the second line are strictly less than n.

Alexander guarantees that the answer exists and does not exceed 1018.

The number k doesn't contain leading zeros.

Output

Print the number x (0 ≤ x ≤ 1018) — the answer to the problem.

Examples

input

13
12

output

12

input

16
11311

output

475

input

20
999

output

3789

input

17
2016

output

594

Note

In the first example 12 could be obtained by converting two numbers to the system with base 13: 12 = 12·130 or 15 = 1·131 + 2·130.

此题有毒。直接贪心，自己电脑上测试数据都过，cf上莫名其妙的变了。。。

 //2016.01.21
 #include <iostream>
 #include <cstdio>
 #include <algorithm>
 #include <cstring>
 #define ll long long

 using namespace std;

 int fun_len(ll a)
 {
     ll n = ;
     while(a)
     {
         n++;
         a/=;
     }
     return n;
 }

 ll pow(ll a, ll b)
 {
     ll ans = ;
     while(b)
     {
         if(b&)ans *= a;
         a*=a;
         b>>=;
     }
 }

 int main()
 {
     ll cnt, dig[];
     ll n;
     string k;
     while(cin>>n>>k)
     {
         cnt = ;
         ll tmp = n, base;
         int len_of_n = , high;
         while(tmp)
         {
             len_of_n++;
             high = tmp%;
             tmp/=;
         }
         memset(dig, , sizeof(dig));
         tmp = , base = ;
         for(int i = k.length()-; i >= ; i--)
         {
             if(k[i]=='')
             {
                 int pos = i;
                 while(k[pos] == '')pos--;
                 int num_of_zero = i-pos;
                 if(tmp!= && ((k[pos]-'')*pow(, num_of_zero+fun_len(tmp))+tmp>=n))dig[cnt++] = tmp;
                 else if(tmp!=){
                     tmp = (k[pos]-'')*pow(, num_of_zero+fun_len(tmp))+tmp;
                     base = pow(, fun_len(tmp));
                     i = pos;
                     if(i==){dig[cnt++] = tmp; break;}
                     continue;
                 }
                 if(num_of_zero<len_of_n-){
                     tmp = (k[pos]-'')*pow(, num_of_zero);
                     base = pow(, num_of_zero+);
                 }
                 else{
                     tmp = (k[pos]-'')*pow(, len_of_n-);
                     int zero = num_of_zero-len_of_n+;
                     if(tmp>=n){
                         tmp/=;
                         zero++;
                     }
                     for(int j = ; j < zero; j++)dig[cnt++] = ;
                     base*=;
                 }
                 if(pos == ){dig[cnt++] = tmp; break;}
                 i = pos-;
                 if(k[i] == ''){i++;continue;}
             }
             if(tmp+base*(k[i]-'')>=n)
             {
                 dig[cnt++] = tmp;
                 tmp = k[i]-'';
                 base = ;
             }else{
                 tmp += base*(k[i]-'');
                 base*=;
             }
             if(i==)dig[cnt++] = tmp;
         }
         ll ans = ;
         base = ;
         for(int i = ; i < cnt; i++)
         {
             ans += base*dig[i];
             base*=n;
         }
         cout<<ans<<endl;
     }

     return ;
 }