Consider the following pseudo-code fragment in which an invariant for the loop is $m \times x^k=p^n$ and $k\ge 0$.

Pre-conditions: $p\ge 1$ and $n\ge 0$

Assume that overflow never occurs.

int x = p;
int k = n;
int m = 1;

while (k != 0) {
if (k is odd) then m = m * x;
x = x * x;
k = floor(k / 2);
}

Which of the following must be true at the end of the while loop?