15296번 - Sum Squared Digits Function 다국어

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 = a₀ + a₁*b + a₂*b² + …

then:

SSD(b, n) = a₀² + a₁² + a₂² + …

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.

The first line of input contains a single decimal integer P, (1 ≤ P ≤ 10000), 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 ≤ b ≤ 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. 

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.