def pathways_ids2pathways_descriptions(pathways_descriptions, genes_and_pathways):
    """
    INPUT:  pathways_descriptions: dict, ex: 
                          {'hsa00010':'Glycolysis / Gluconeogenesis'} 
            genes_and_pathways: dict, ex:
                          {10:['hsa00232', 'hsa00983', 'hsa01100', 'hsa05204']}
    OUTPUT: dict mapping genes to pathways description, ex:
                          {10: ['Glycolysis / Gluconeogenesis', ...]}
    """
    genes_and_pathways_description = {}
    for gene in genes_and_pathways:
        pathways_ids = genes_and_pathways[gene]
        for pathways_id in pathways_ids:
            pathway_description = pathways_descriptions[pathways_id]
            if gene in genes_and_pathways_description:
                genes_and_pathways_description[gene].append(pathway_description)
            else:
                genes_and_pathways_description[gene] = [pathway_description]
    return genes_and_pathways_description