- Prepare
- Algorithms
- Recursion
- Recursive Digit Sum

# Recursive Digit Sum

# Recursive Digit Sum

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

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

- If has only digit, then its super digit is .
- Otherwise, the super digit of is equal to the super digit of the sum of the digits of .

For example, the super digit of will be calculated as:

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

**Example**

The number is created by concatenating the string times so the initial .

```
superDigit(p) = superDigit(9875987598759875)
9+8+7+5+9+8+7+5+9+8+7+5+9+8+7+5 = 116
superDigit(p) = superDigit(116)
1+1+6 = 8
superDigit(p) = superDigit(8)
```

All of the digits of sum to . The digits of sum to . is only one digit, so it is the super digit.

**Function Description**

Complete the function *superDigit* in the editor below. It must return the calculated super digit as an integer.

superDigit has the following parameter(s):

*string n:*a string representation of an integer*int k:*the times to concatenate to make

**Returns**

*int:*the super digit of repeated times

**Input Format**

The first line contains two space separated integers, and .

**Constraints**

**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
```

**Sample Input 1**

```
9875 4
```

**Sample Output 1**

```
8
```

**Sample Input 2**

```
123 3
```

**Sample Output 2**

```
9
```

**Explanation 2**

Here and , so .

```
super_digit(P) = super_digit(123123123)
= super_digit(1+2+3+1+2+3+1+2+3)
= super_digit(18)
= super_digit(1+8)
= super_digit(9)
= 9
```