from typing import Dict


def dendrogram_height(merging_similarities: Dict[int, float], m: int) -> Dict[int, float]:
    """
    Find dendrogram height, defined with a recursive sum of the reciprocal of the merging scores.

    :param merging_similarities: merging scores of the algorithm.
    :param m: initial number of clusters.
    :return: dendrogram height.
    """
    dh = {m - 1: (1 / merging_similarities[m - 1])}

    for i in list(merging_similarities.keys())[:-1]:
        dh[i - 1] = dh[i] + 1 / merging_similarities[i - 1]

    return dh