Let f be a one$-$way function. Define a function B $\{0,1\}\{0,1\}$ for f$,$ where B$($x$)$ outputs the inner product modulo $2$ of the first $$x$/2$ bits of x and the last $$x$/2$ bits of x$.$ Prove or disprove that B is necessarily a hard$-$core predicate for f$.$