diff --git a/src/index/sparse/sparse_inverted_index.h b/src/index/sparse/sparse_inverted_index.h
index 06665894a..cb891c89e 100644
--- a/src/index/sparse/sparse_inverted_index.h
+++ b/src/index/sparse/sparse_inverted_index.h
@@ -654,16 +654,16 @@ class InvertedIndex : public BaseInvertedIndex<T> {
             std::sort(cursors.begin(), cursors.end(), [](auto& x, auto& y) { return x->cur_vec_id_ < y->cur_vec_id_; });
         };
         sort_cursors();
+        float upper_bound = 0;
+        size_t pivot_cursor_id = 0;
         while (true) {
             float threshold = heap.full() ? heap.top().val : 0;
-            float upper_bound = 0;
-            size_t pivot;
             bool found_pivot = false;
-            for (pivot = 0; pivot < valid_q_dim; ++pivot) {
-                if (cursors[pivot]->loc_ >= cursors[pivot]->lut_size_) {
+            for (; pivot_cursor_id < valid_q_dim; ++pivot_cursor_id) {
+                if (cursors[pivot_cursor_id]->loc_ >= cursors[pivot_cursor_id]->lut_size_) {
                     break;
                 }
-                upper_bound += cursors[pivot]->max_score_;
+                upper_bound += cursors[pivot_cursor_id]->max_score_;
                 if (upper_bound > threshold) {
                     found_pivot = true;
                     break;
@@ -672,24 +672,35 @@ class InvertedIndex : public BaseInvertedIndex<T> {
             if (!found_pivot) {
                 break;
             }
-            table_t pivot_id = cursors[pivot]->cur_vec_id_;
-            if (pivot_id == cursors[0]->cur_vec_id_) {
-                float score = 0;
+            table_t pivot_vec_id = cursors[pivot_cursor_id]->cur_vec_id_;
+            if (pivot_vec_id == cursors[0]->cur_vec_id_) {
+                float score_sum = 0;
                 for (auto& cursor : cursors) {
-                    if (cursor->cur_vec_id_ != pivot_id) {
+                    if (cursor->cur_vec_id_ != pivot_vec_id) {
                         break;
                     }
                     T cur_vec_sum = bm25 ? bm25_params_->row_sums.at(cursor->cur_vec_id_) : 0;
-                    score += cursor->q_value_ * computer(cursor->cur_vec_val(), cur_vec_sum);
+                    score_sum += cursor->q_value_ * computer(cursor->cur_vec_val(), cur_vec_sum);
                     cursor->next();
                 }
-                heap.push(pivot_id, score);
+                heap.push(pivot_vec_id, score_sum);
                 sort_cursors();
+                pivot_cursor_id = 0;
+                upper_bound = 0;
             } else {
-                size_t next_list = pivot;
-                for (; cursors[next_list]->cur_vec_id_ == pivot_id; --next_list) {
+                size_t next_list = pivot_cursor_id;
+                for (; cursors[next_list]->cur_vec_id_ == pivot_vec_id; --next_list) {
+                }
+                cursors[next_list]->seek(pivot_vec_id);
+                if (cursors[next_list]->cur_vec_id_ > pivot_vec_id) {
+                    upper_bound -= cursors[next_list]->max_score_;
+                    upper_bound -= cursors[pivot_cursor_id]->max_score_;
+                    --pivot_cursor_id;
+                } else {
+                    // the max_score_ of the pivot will be added again in the next loop,
+                    // so it needs to be subtracted here.
+                    upper_bound -= cursors[pivot_cursor_id]->max_score_;
                 }
-                cursors[next_list]->seek(pivot_id);
                 for (size_t i = next_list + 1; i < valid_q_dim; ++i) {
                     if (cursors[i]->cur_vec_id_ >= cursors[i - 1]->cur_vec_id_) {
                         break;