Getting original mesh cell index mapped to boundary mesh

I have generated the boundary mesh from original 3D mesh. In the boundary mesh element, how can I get the corresponding cell index of original mesh? The MWE is:

from dolfin import *
bdim = dim-1
bmesh = BoundaryMesh(mesh, "exterior")
mapping = bmesh.entity_map(bdim)
# Get mapped index from original mesh
for cell in cells(bmesh):
# Output is much different from corresponding original mesh. 

I tried looking for options to get original cell index related to boundary mesh (index). But, getting difficulty to find it. Any help is greatly appreciated.
Edit: I apologize for not putting problem in manner required to get answered. Any resources related to the problem would help. Thanks.

I figured out that mapping=bmesh.entity_map(bdim) was giving facet mapping of original mesh. There I extracted the connectivity with cells of original mesh. Here is the code that worked for me.

connect_mesh = dict()
connect_mesh2 = []
for c in cells(mesh):
    for f in facets(c):