Find clusters with Lloyd's algorithm. k-means normally seeds its centroids at random, but this problem has no randomness — the initialization is fixed so the answer is unique.

Input

X      # (n, d) real-valued features
k      # cluster count (at least 1, at most n)
iters  # iteration count (0 or more)

If X arrives one-dimensional, treat it as (n, 1).

Algorithm

• The initial centroids are the first k rows of X. They are not sampled.
• Repeat these two steps exactly iters times:
  1. Assign — attach each point to its nearest centroid (Euclidean, square root included). On equal distance, the lower centroid index wins.
  2. Update — move each centroid to the mean of its cluster.
• An empty cluster keeps its centroid — if no point is assigned to it, leave the coordinates as they were. Without this rule you divide by zero.

With iters=0 the initial centroids are the answer.

Return

kmeans(X, k, iters) → a list of k centroid coordinates (each a list of length d), every float rounded to 6 decimal places.

Implement kmeans(X, k, iters).

• The initial centroids are the first k rows of X — not random.
• Assign, then update, exactly iters times.
• On a distance tie, the lower centroid index wins.
• An empty cluster keeps its centroid (do not divide by zero).
• Return k coordinate lists, each value round(v, 6).