diff --git a/library/data_structures_[l,r)/seg_tree_uncommon/implicit.hpp b/library/data_structures_[l,r)/seg_tree_uncommon/implicit.hpp
index 3d2648c4..cdd51142 100644
--- a/library/data_structures_[l,r)/seg_tree_uncommon/implicit.hpp
+++ b/library/data_structures_[l,r)/seg_tree_uncommon/implicit.hpp
@@ -42,7 +42,7 @@ template<int N> struct implicit_seg_tree {
     int v) {
     if (r <= tl || tr <= l) return;
     if (l <= tl && tr <= r) return apply(add, v);
-    int tm = tl + (tr - tl) / 2;
+    int tm = midpoint(tl, tr);
     push(tl, tm, tr, v);
     update(l, r, add, tl, tm, tree[v].lch);
     update(l, r, add, tm, tr, tree[v].rch);
@@ -55,7 +55,7 @@ template<int N> struct implicit_seg_tree {
   dt query(int l, int r, int tl, int tr, int v) {
     if (r <= tl || tr <= l) return unit;
     if (l <= tl && tr <= r) return tree[v].num;
-    int tm = tl + (tr - tl) / 2;
+    int tm = midpoint(tl, tr);
     push(tl, tm, tr, v);
     return op(query(l, r, tl, tm, tree[v].lch),
       query(l, r, tm, tr, tree[v].rch));
diff --git a/library/data_structures_[l,r)/seg_tree_uncommon/kth_smallest_query.hpp b/library/data_structures_[l,r)/seg_tree_uncommon/kth_smallest_query.hpp
index 09aff8cc..1aeca186 100644
--- a/library/data_structures_[l,r)/seg_tree_uncommon/kth_smallest_query.hpp
+++ b/library/data_structures_[l,r)/seg_tree_uncommon/kth_smallest_query.hpp
@@ -25,7 +25,7 @@ struct kth_smallest {
   }
   int query(int k, int tl, int tr, int vl, int vr) {
     if (tr - tl == 1) return tl;
-    int tm = tl + (tr - tl) / 2;
+    int tm = midpoint(tl, tr);
     int cnt_l = pst.tree[pst.tree[vr].lch].sum -
                 pst.tree[pst.tree[vl].lch].sum;
     if (cnt_l >= k)
diff --git a/library/data_structures_[l,r)/seg_tree_uncommon/persistent.hpp b/library/data_structures_[l,r)/seg_tree_uncommon/persistent.hpp
index 151cda92..f59ad519 100644
--- a/library/data_structures_[l,r)/seg_tree_uncommon/persistent.hpp
+++ b/library/data_structures_[l,r)/seg_tree_uncommon/persistent.hpp
@@ -30,7 +30,7 @@ struct PST {
       tree.emplace_back(tree[v].sum + change, 0, 0);
       return sz(tree) - 1;
     }
-    int tm = tl + (tr - tl) / 2;
+    int tm = midpoint(tl, tr);
     int lch = tree[v].lch;
     int rch = tree[v].rch;
     if (idx < tm) lch = update(idx, change, tl, tm, lch);
@@ -45,7 +45,7 @@ struct PST {
   ll query(int l, int r, int tl, int tr, int v) {
     if (v == 0 || r <= tl || tr <= l) return 0;
     if (l <= tl && tr <= r) return tree[v].sum;
-    int tm = tl + (tr - tl) / 2;
+    int tm = midpoint(tl, tr);
     return query(l, r, tl, tm, tree[v].lch) +
            query(l, r, tm, tr, tree[v].rch);
   }
diff --git a/library/math/num_distinct_subsequences.hpp b/library/math/num_distinct_subsequences.hpp
index 2ff86242..301c10be 100644
--- a/library/math/num_distinct_subsequences.hpp
+++ b/library/math/num_distinct_subsequences.hpp
@@ -9,12 +9,11 @@ int num_subsequences(const vi& a, int mod) {
   rep(i, 0, sz(a)) {
     int& cur = dp[i + 1] = 2 * dp[i];
     if (cur >= mod) cur -= mod;
-    auto it = last.find(a[i]);
-    if (it != end(last)) {
-      cur -= dp[it->second];
+    auto [it, ins] = last.emplace(a[i], i);
+    if (!ins) {
+      cur -= dp[exchange(it->second, i)];
       if (cur < 0) cur += mod;
-      it->second = i;
-    } else last[a[i]] = i;
+    }
   }
   return dp.back();
 }