The most naive way of computing n¹⁵ requires fourteen multiplications:

n n ... n = n¹⁵

But using a "binary" method you can compute it in six multiplications:

n n = n²
n² n² = n⁴
n⁴ n⁴ = n⁸
n⁸ n⁴ = n¹²
n¹² n² = n¹⁴
n¹⁴ n = n¹⁵

However it is yet possible to compute it in only five multiplications:

n n = n²
n² n = n³
n³ n³ = n⁶
n⁶ n⁶ = n¹²
n¹² n³ = n¹⁵

We shall define m(k) to be the minimum number of multiplications to compute n^k; for example m(15) = 5.

For 1 k 200, find m(k).