use Filter to bring Null andNon-@CAP_FIRST$null data to select

Question

Controller:

public function get(Request $request, Funcionario $funcionarios)
{
    if ($funcionarios->id) {
        return response()->json(['data' =$funcionarios->toArray()]);
    }

    $rules = [
        'nome' =['type' ='string', 'op' ='like', 'prefix' ='%', 'suffix' ='%'],
        'celular' =['type' ='string', 'op' ='like', 'prefix' ='%', 'suffix' ='%'],
        'telefone' =['type' ='string', 'op' ='like', 'prefix' ='%', 'suffix' ='%'],
        'email' =['type' ='string', 'op' ='like', 'prefix' ='%', 'suffix' ='%'],
        'idprofessor' =['type' ='integer', 'op' ='=', 'prefix' ='', 'suffix' ='']
    ];

    $query = Funcionario::query();

    $query = Utils::orderBy($query, $request->get('order'));
    $query = Utils::filter($query, $request->get('filter', []), $rules);

    return response()->json($query->paginate($request->get('limit')));
}

View VUE

activeOptions: [{ label: 'Todos', key: '' }, { label: 'Colaboradores',
key: 'NULL' }, { label: 'Docentes', key: '' }],

---

<div class="filter-container"     <el-input
:placeholder="$t('employee.name')" v-model="listQuery.filter.nome"
style="width: 200px;" class="filter-item"
@keyup.enter.native="handleFilter"/>
      <el-input :placeholder="$t('employee.cell')" v-model="listQuery.filter.celular" style="width: 200px;"
class="filter-item" @keyup.enter.native="handleFilter"/>
      <el-input :placeholder="$t('employee.phone')" v-model="listQuery.filter.telefone" style="width: 200px;"
class="filter-item" @keyup.enter.native="handleFilter"/>
      <el-select v-model="listQuery.filter.jacad_idprofessor" clearable style="width: 140px" class="filter-item"
@change="handleFilter">
        <el-option v-for="item in activeOptions" :key="item.key" :label="item.label" :value="item.key"/>
      </el-select>
      <el-button v-waves class="filter-item" type="primary" icon="el-icon-search" @click="handleFilter">{{ $t('table.search')
}}</el-button>
      <el-button v-waves :loading="downloadLoading" class="filter-item" type="primary" icon="el-icon-download"
@click="handleDownload">{{ $t('table.export') }}</el-button>
      <router-link target="_blank" to="/employee/printer">
        <el-button type="primary" class="filter-item" icon="el-icon-printer">{{ $t('table.printer') }}</el-button>
      </router-link>
</div>

I need to bring, in select the Collaborators who are NULL and teachers who are not null, that field is integer.