Show that a standard turing machine $($turing machine with $1$ tape$)$ is equivalent in expressive and computational power to a turing machine that has $1$ tape and a counter that can hold any integer $($up to infinity$).$ You can prove this by simulating the $2$nd version of the turing machine $($tape $+$ counter$)$ on the $1$st version $($just $1$ tape$).$ Feel free to use any previously defined lemmas $($for example $-$ a multi tape turing machine is equivalent to a single tape turing machine etc.$)$