pub fn non_same_query_pcs_sumcheck_witness<'a, F, PW, Backend>(
    witness_index: &mut MultilinearExtensionIndex<'a, PW::Underlier, PW::Scalar>,
    memoized_queries: &mut MemoizedQueries<PW, Backend>,
    meta: NonSameQueryPcsClaimMeta<F>,
    backend: Backend
) -> Result<BivariateSumcheckWitness<'a, PW>, Error>
where F: Field + From<PW::Scalar>, PW: PackedField + WithUnderlier, PW::Scalar: From<F> + TowerField, PW::Underlier: PackScalar<PW::Scalar, Packed = PW>, Backend: ComputationBackend,