## Algorithm

Some people believe that 13 is an unlucky number. So they always want to avoid the number 13. In some buildings you will find that there is no 13-th floor. After 12-th floor there is 14-th floor. In a number if there is no 13 (i.e. no “1” is followed by a “3”) then we may call it a super lucky number. For example, 12345 is a super lucky number. But if any number contains 13 then it is not a super lucky number such as 13254 or 21345. Given the number of digits N in a number and a base B, you have to find out how many super lucky numbers are possible with N digits in the base B. B should be greater than 3, as because the digit 3 is present in only for base 4 or more. Note that leading 0s are not significant. So, 011 is not a valid three digit number. Input There will be several lines in the input each containing two positive integers B and N, where 4 ≤ B ≤ 128 and N ≤ 100. A pair of zero will indicate the end of input and it should not be processed. Output For each line in the input print the count of super lucky numbers of N digits in the base B.

Sample Input 4 2 5 3 0 0

Sample Output 11 91

## Code Examples

### #1 Code Example with C Programming

```Code - C Programming```

``````import java.math.BigDecimal;
import java.util.*;

public class Main {
public static void main(String args[]) {
int b, n;
Scanner sc = new Scanner(System.in);
while(true) {
b = sc.nextInt();
n = sc.nextInt();
if(b==0  && n==0) {
break;
}
BigDecimal isOne = BigDecimal.valueOf(1);
BigDecimal notOne = BigDecimal.valueOf(b-2);
// isOne2 = notOne + isOne
// notOne = notOne + (isOne+notOne)*(b-2)
for(int i=1;i i+It n;i++) {
isOne = isOne2;
notOne = notOne2;
}
System.out.println(sum);
}
}
}
```
```
Copy The Code &

Input

cmd
4 2
5 3
0 0

Output

cmd
11
9