A company suggests the following hash function: Let p $>=3$ be a large prime with respect to which the discrete logarithm problem is intractable in $\_$p$^*.$ Let g$\_1,$ g$\_2$ in $\_$p$^*$ be two distinct generators of $\_$p$^*.$ Define H : $\_$p$-1\backslash$times $\_$p$-1\_$p$^*$ as H$($x$\_1,$ x$\_2)=($g$\_1^$x$\_1$ g$\_2^$x$\_2)$ p The company claims that this hash function is collision$-$resistant. Prove that they are wrong. Namely, present an algorithm C that given any p$,$ g$\_1,$ g$\_2$ that satisfy the above conditions very easily $($formally$,$ in time polynomial in $|$p$|)$ outputs two pairs $($x$\_1,$ x$\_2),($x$\_1^\text{'},$ x$\_2^\text{'})$ such that: $-($x$\_1,$ x$\_2)$ in $\_$p$-1\backslash$times $\_$p$-1,-($x$\_1^\text{'},$ x$\_2^\text{'})$ in $\_$p$-1\backslash$times $\_$p$-1,$ and $-$ H$($x$\_1,$ x$\_2)=$H$($x$\_1^\text{'},$ x$\_2^\text{'}),$ but $-($x$\_1,$ x$\_2)!=($x$\_1^\text{'},$ x$\_2^\text{'}).$ Be sure to justify your answer. Hint: Recalling the formula for calculating the Legendre symbol may be useful.