C# - Cannot Pass A Input From Text Box To A Query String And Then Keep The String In This Box?

I have a simple ASP.net page:

<form id="form1" runat="server">
<p><asp:TextBox id="input_box" runat="server"></asp:TextBox>
<asp:Button Text="OK" runat="server" OnClick="run" /></p>
</form>

I want to send input from input_box to a query string, and then keep this input in the input_box when the page reloads.

That's the code behind page:

protected void Page_Load(object sender, EventArgs e)
{
input_box.Text = Request.QueryString["input"];
}
protected void run(object sender, EventArgs e)
{
string url = string.Format("?input={0}", input_box.Text);
Response.Redirect(Request.Url.AbsolutePath + url);
}

Problem is that when query string is not empty, string from input_box cannot be passed to query string. How to correct it?