Other / Removed from syllabus

The following function computes $X^Y$ for positive integers X and Y.

int exp(int X, int Y) {
    int res = 1, a = X, b = Y;

    while ( b != 0 ){
        if ( b%2 == 0) { a = a*a; b = b/2; }
        else           { res = res*a; b = b-1; }
    }
    return res;
}

Which one of the following conditions is TRUE before every iteration of the loop?

Suppose $c = \langle c[0], \ldots, c[k-1] \rangle$ 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 ← z² mod n
    if c[i] = 1
        then z ← (z × a) mod n
return z

If $k = 4$, $c = \langle 1, 0, 1, 1 \rangle$, $a = 2$ and $n = 8$, then the output of DOSOMETHING$(c, a, n)$ is _____.