For some prime numbers p and q where 
, a rational function R, is defined as follows: 
. Using the output 
, another rational function K, is defined: 
. Finaly, using the output 
, we define the function N: 
; where the symbol "
", represents the integer part of the decimal expansion of the fraction k .
, a rational function R, is defined as follows: . Using the output , another rational function K, is defined: . Finaly, using the output , we define the function N: ; where the symbol "", represents the integer part of the decimal expansion of the fraction k .For example for 
and 
: 
; 
; since 
, 
.
and : ; ; since , .And, for 
and 
: 
; 
; since
, 
.
and : ; ; since, .If 
, and given an integer limit x, write a function that returns a sorted array of all unique values of n that are less than or equal to x.
, and given an integer limit x, write a function that returns a sorted array of all unique values of n that are less than or equal to x.-----------
HINT: Both R and K, are rational functions and expect exact rational fraction outputs. Therefore, please preserve numerators and denominators for R and K, and evaluate decimal expansions only when calculating the output of the function N.
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