Suppose $c = \langle c[0], ..., c[k - 1]\rangle$ is an array of length $k$, where all the entries are from the set $\{0, 1\}$. For any positive integers $a$ and $n$, consider the following pseudocode.DOSOMETHING (c, a, n) z ← 1 for i ← 0 to k - 1 do z ← z^2 mod n if c[i] = 1 then z ← (z × a) mod n return zIf $k = 4, c = \langle 1, 0, 1, 1\rangle, a = 2$ and $n = 8$, then the output of DOSOMETHING$(c, a, n)$ is _________.

We can trace the execution of DOSOMETHING(c, a, n) with $k = 4$, $c = \langle 1, 0, 1, 1 \rangle$, $a = 2$, and $n = 8$:

• Initially:

  $$z = 1$$

• Iteration $i = 0$ ($c[0] = 1$):

  • $z \leftarrow z^2 \bmod 8 = 1^2 \bmod 8 = 1$

  • Since $c[0] = 1$: $z \leftarrow (z \times a) \bmod 8 = (1 \times 2) \bmod 8 = 2$

• Iteration $i = 1$ ($c[1] = 0$):

  • $z \leftarrow z^2 \bmod 8 = 2^2 \bmod 8 = 4$

  • Since $c[1] = 0$, the if condition is false.

• Iteration $i = 2$ ($c[2] = 1$):

  • $z \leftarrow z^2 \bmod 8 = 4^2 \bmod 8 = 16 \bmod 8 = 0$

  • Since $c[2] = 1$: $z \leftarrow (z \times a) \bmod 8 = (0 \times 2) \bmod 8 = 0$

• Iteration $i = 3$ ($c[3] = 1$):

  • $z \leftarrow z^2 \bmod 8 = 0^2 \bmod 8 = 0$

  • Since $c[3] = 1$: $z \leftarrow (z \times a) \bmod 8 = (0 \times 2) \bmod 8 = 0$

After all iterations, the returned value of $z$ is 0.