Updating parent control passes changes to child control

Using Streamlit
1

I want to implement below, but failed:
1 pass a selected value from a parent control to a child control. The child control UI displays the new value
2 changing the child control value doesn’t affect parent control.

Below is what I did, but it is not working in that parent control create a new child control every time, yet not passing value to the existing child control.

import streamlit as st

@st.fragment
def create_dd():
    # with st.container():
    data = []
    with st.container():
        options = st.multiselect(
            "Parent list",
            ["a", "b", "c",],
            data
            , key='ms_1'
        )
        st.session_state.dd = options
        st.write("Parent selected:", options)
        if options:
            create_dd2()

@st.fragment
def create_dd2():
    data = []
    if 'dd' in st.session_state:
        data = st.session_state.dd

    with st.container():
        options2 = st.multiselect(
            "Child list",
            ["a", "b", "c"],
            data
            ,key='ms_2'
        )
        st.write("Child selected:", options2)

create_dd()
create_dd2()

any idea?