How to use Higher Rank Trait Bounds with anonymous closure in return type

Is it possible to return FnMut closure that takes reference and return reference with same lifetime as it takes?

fn fun(buf: &mut [f32], mut idx: usize) -> impl FnMut(&[i16]) -> &[i16] {
    |input| {
        buf[idx] = input[0] as f32;
        idx += 1;
        &input[1..]
    }
}

I've tried things like impl for<'a> FnMut(&'a [i16]) -> &'a [i16]) and it gives

error[E0482]: lifetime of return value does not outlive the function call
 --> src/main.rs:1:44
  |
1 | fn fun(buf: &mut [f32], mut idx: usize) -> impl for<'a> FnMut(&'a [i16]) -> &'a [i16] {
  |                                            ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
  |
note: the return value is only valid for the anonymous lifetime defined on the function body at 1:13
 --> src/main.rs:1:13
  |
1 | fn fun(buf: &mut [f32], mut idx: usize) -> impl for<'a> FnMut(&'a [i16]) -> &'a [i16] {
  |             ^^^^^^^^^^

• The returned function should capture buf by value (i.e., use move)
• The returned function must not outlive buf (having the lifetime 'buf in the below snippet):

So:

fn fun<'buf>(buf: &'buf mut [f32], mut idx: usize) -> impl FnMut(&[i16]) -> &[i16] + 'buf {
    move |input| {
        buf[idx] = input[0] as f32;
        idx += 1;
        &input[1..]
    }
}