code javascript:

Given a subset of a series of dice roll results, and the arithmetic mean of all results, find the missing results.

Task description

You have just rolled a dice several times. The N roll results that you remember are described by an array A$.$ However, there are F rolls whose results you have forgotten. The arithmetic mean of all of the roll results $($the sum of all the roll results divided by the number of rolls$)$ equals M$.$

What are the possible results of the missing rolls?

Write a function:

function solution$($A$,$ F$,$ M$)$;

that, given an array A of length N$,$ an integer F and an integer M$,$ returns an array containing possible results of the missed rolls. The returned array should contain F integers from $1$ to $6($valid dice rolls$).$ If such an array does not exist then the function should return $[0].$

Examples:

$1.$ Given A $=[3,2,4,3],$ F $=2,$ M $=4,$ your function should return $[6,6].$ The arithmetic mean of all the rolls is $(3+2+4+3+6+6)/6=24/6=4.$

$2.$ Given A $=[1,5,6],$ F $=4,$ M $=3,$ your function may return $[2,1,2,4]$ or $[6,1,1,1]($among others$).$

$3.$ Given A $=[1,2,3,4],$ F $=4,$ M $=6,$ your function should return $[0].$ It is not possible to obtain such a mean.

$4.$ Given A $=[6,1],$ F $=1,$ M $=1,$ your function should return $[0].$ It is not possible to obtain such a mean.

Write an efficient algorithm for the following assumptions:

$$ N and F are integers within the range $[1.\mathrm{.}100,000]$;

$$ each element of array A is an integer within the range $[1.\mathrm{.}6]$;

$$ M is an integer within the range $[1.\mathrm{.}6].$

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