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:

Given $A=[3,2,4,3],F=2,M=4,$ your function should return $6,6.$ The arithmetic mean of all the rolls is $\frac{3+2+4+3+6+6}{6}=\frac{24}{6}=4.$

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

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

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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