How to preserve widget values with st.switch_page

Using Streamlit
1

my code like this:

# File       : main.py
import streamlit as st

if __name__ == "__main__":
    st.set_page_config(layout="wide")

    st.markdown(
        """
        <style>
        #MainMenu {visibility: hidden;}
        footer {visibility: hidden;}
        </style>
        """,
        unsafe_allow_html=True
    )

    pg = st.navigation(
        [
            st.Page("st_pages/page_1.py", title="**Page1**", url_path="Summarize"),
            st.Page("st_pages/page_2.py", title="**Page2**", url_path="Search", default=False),
            st.Page("st_pages/page_3.py", title="**Page3**", url_path="Detail", default=False),
        ],
        position="hidden"

    )

    with st.sidebar:
        st.radio("What's your name?", ("**A**", "**B**"),
                 label_visibility="collapsed", key="r_value", index=0)
        display_project = st.session_state.get("r_value", "**Demo**")
        st.caption(f"Current Value：:green[{display_project}]")

        st.divider()

        st.page_link("st_pages/page_1.py", label="**Page1**")
        st.page_link("st_pages/page_3.py", label="**Page3**")
        st.divider()

    pg.run()```

File : st_pages/page_1.py

import streamlit as st

if name == ‘page’:
btn = st.button(“Switch”)
if btn:
st.switch_page(“st_pages/page_2.py”)

File : st_pages/page_2.py

import streamlit as st

if name == ‘page’:
st.write(“Current Page: page_2”)


When I set radio value then switch page, the radio value change to default value. How can I reslove this problem?