Problem D
Sum Squared Digits Function
The Sum Squared Digits function, $SSD(b, n)$ of a positive integer $n$, in base $b$ is defined by representing $n$ in base $b$ as in:
\[ n = a_0 + a_1 * b + a_2 * b^2 + \ldots \]then:
\[ SSD(b, n) = a_0^2 + a_1^2 + a_2^2 + \ldots \]is the sum of squares of the digits of the representation.
Write a program to compute the Sum Squared Digits function of an input positive number.
Input
The first line of input contains a single decimal integer $P$, ($1 \le P \le 1\, 000$), which is the number of data sets that follow. Each data set should be processed identically and independently.
Each data set consists of a single line of input. It contains the data set number, $K$, followed by the base, $b$ ($3 \le b \le 16$) as a decimal integer, followed by the positive integer, $n$ (as a decimal integer) for which the Sum Squared Digits function is to be computed with respect to the base $b$. $n$ will fit in a $32$ bit unsigned integer. The data set number $K$ starts at $1$ and is incremented by $1$ for each data set.
Output
For each data set there is a single line of output.
The single line of output consists of the data set number, $K$, followed by a single space followed by the value of $SSD(b, n)$ as a decimal integer.
| Sample Input 1 | Sample Output 1 |
|---|---|
3 1 10 1234 2 3 98765 3 16 987654321 |
1 30 2 19 3 696 |