$(15$ points$)$ Write a program that takes two integers from its user $($say $n$ and $m)$ and constructs an $n-$by$-$m integer matrix as follows: $($i$)$ the first row of the matrix should contain randomly selected $n$ unique numbers between and including $1$ and $50,$ and $($ii$)$ each other row of the matrix should contain the twice of its preceding row. Your program should then display the contents of this constructed matrix.

For example, if $n$ and $m$ are $3$ and $4,$ respectively, the following can be a possible output of such a program.

$\backslash$table$[[5,30,9,25],[10,60,18,50],[20,120,36,100]]$

You may assume that $n$ will be smaller than $50.($in c$++)$