## Recursive Digit Sum

by wanbo

Given an integer, we need to find the super digit of the integer.

We define super digit of an integer using the following rules:

- If has only digit, then its super digit is .
- Otherwise, the super digit of is equal to the super digit of the digit-sum of . Here, digit-sum of a number is defined as the sum of its digits.

For example, super digit of will be calculated as:

```
super_digit(9875) = super_digit(9+8+7+5)
= super_digit(29)
= super_digit(2+9)
= super_digit(11)
= super_digit(1+1)
= super_digit(2)
= 2.
```

You are given two numbers and . You have to calculate the super digit of .

is created when number is concatenated times. That is, if and , then .

**Input Format**

The first line contains two space separated integers, and .

**Constraints**

**Output Format**

Output the super digit of , where is created as described above.

**Sample Input 0**

```
148 3
```

**Sample Output 0**

```
3
```

**Explanation 0**

Here and , so .

```
super_digit(P) = super_digit(148148148)
= super_digit(1+4+8+1+4+8+1+4+8)
= super_digit(39)
= super_digit(3+9)
= super_digit(12)
= super_digit(1+2)
= super_digit(3)
= 3.
```