For positive integers k and n, the k-power remainder of n is defined as r in the following equation:
n = k^w + r, where w is the largest integer such that r is not negative. For instance, the 3-power remainder of 13 is 4, since 13 = 3^2 + 4. In terms of k and w, what is the largest possible value of r that satisfies the given conditions?	Choose the most appropriate option:
A) (k – 1)k^w – 1
B) k^w – 1
C) (k + 1)k^w – 1
D) k^(w+1) – 1
E) (k + 1)k^(w+1) – 1
n = k^w + r, where w is the largest integer such that r is not negative   This means k^w &lt;= n, and k^(w+1) &gt; n   So n lies between k^w and k^(w+1)   Now, r = n - k^w, which means r is the distance between n and k^w   This distance is maximised at the highest possible value of n, which can be just below k^(w+1)   So n = k^(w+1) - 1, as n is an integer   Therefore, highest value of r = n - k^w = k^(w+1) - 1 - k^w = (k - 1)k^w - 1   (k – 1)k^w – 1 is the correct
<result>A</result>
For positive integers k and n, the k-power remainder of n is defined as r in the following equation:
n = k^w + r, where w is the largest integer such that r is not negative. For instance, the 3-power remainder of 13 is 4, since 13 = 3^2 + 4. In terms of k and w, what is the largest possible value of r that satisfies the given conditions?