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DS-1000 / 805 / After clustering a distance matrix with scipy.cluster.hierarchy.linkage, and…

Problem

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Problem:
After clustering a distance matrix with scipy.cluster.hierarchy.linkage, and assigning each sample to a cluster using scipy.cluster.hierarchy.cut_tree, I would like to extract one element out of each cluster, which is the k-th closest to that cluster's centroid.
•	I would be the happiest if an off-the-shelf function existed for this, but in the lack thereof:
•	some suggestions were already proposed here for extracting the centroids themselves, but not the closest-to-centroid elements.
•	Note that this is not to be confused with the centroid linkage rule in scipy.cluster.hierarchy.linkage. I have already carried out the clustering itself, just want to access the closest-to-centroid elements.
What I want is the index of the k-closest element in original data for each cluster, i.e., result[0] is the index of the k-th closest element to centroid of cluster 0.
A:
<code>
import numpy as np
import scipy.spatial
centroids = np.random.rand(5, 3)
data = np.random.rand(100, 3)
k = 3
</code>
result = ... # put solution in this variable
BEGIN SOLUTION
<code>

library

Scipy

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Source and history

upstream_id / Original problem ID
805
task_id
1f22db5c-5e57-54ba-ad76-21d806b855f9
task_key
default--test--805
task_revision_id
1
config / split
default / test

Official source

initial import