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We define super digit of an integer x using the following rules:
Given an integer, we need to find the super digit of the integer.
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If x has only 1 digit, then its super digit is x.
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Otherwise, the super digit of x is equal to the super digit of the sum of the digits of x.
For example, the super digit of 9875 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
n='9875'
k=4
The number p is created by concatenating the string n k times so the initial p = 9875987598759875.
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 p sum to 116. The digits of 116 sum to 8. 8 is only one digit, so it is the super digit.