Relationship Between Integer Expressions

Let $k$ be an integer such that when $k$ is divided by $8$, the remainder is $3$:

1. $k ext{ mod } 8 = 3$

2. The integer $m$ is defined as $m = 2k + 5$.

Determine the relationship between the two quantities below:

Quantity A: $m$

Quantity B: The minimum possible value of $m$ when $k$ takes on values that satisfy the first condition.