In this problem we discuss the security of performing one$-$time pad encryption twice:

$($a$)$ Consider the following subroutine that models the result of applying one$-$time pad

encryption with two independent keys:

eavesdrop$0$

$($m in $\{0,1\}$

$\backslash$lambda

$)$:

k$1\{0,1\}$

$\backslash$lambda

k$2\{0,1\}$

$\backslash$lambda

c :$=$ k$2($k$1$ m$)$

return c

$.$

Show that the output of this subroutine is uniformly distributed in $\{0,1\}$

$\backslash$lambda

$.$