Let $f(x)$ be a function of real variable and let $f$ be the function $f(x)=f(x+1)-f(x).$

For $k>1,$ put ${}^{k}f=({}^{k-1}f).$ Then ${}^{k}f(x),$ equals

A$.{\displaystyle \underset{j=0}{\overset{k}{}}}(-1{)}^j(\frac{k}{j})f(x+j)$

B$.{\displaystyle \underset{j=0}{\overset{k}{}}}(-1{)}^{j+1}(\frac{k}{j})f(x+j)$

C$.{\displaystyle \underset{j=0}{\overset{k}{}}}(-1{)}^j(\frac{k}{j})f(x+k-j)$

D$.{\displaystyle \underset{j=0}{\overset{k}{}}}(-1{)}^{j+1}(\frac{k}{j})f(x+k-j)$