another idea

Author: lrvideckis

library/data_structures_[l,r]/seg_tree_uncommon/walk.hpp

@@ -1,8 +1,10 @@
 int walk(int l, int r, const auto& f) {
-  while (l <= r) {
-    int u = l + n, v = __lg(min(u & -u, r - l + 1));
-    if (f(s[u >> v])) l += 1 << v;
-    else r = l + (1 << v) - 2;
-  }
-  return l;
+  l += n, r += n;
+  if (T x = s[l]; f(x))
+    for (l++; l <= r;) {
+      int v = __lg(min(l & -l, r - l + 1));
+      if (T y = op(x, s[l >> v]); f(y)) l += 1 << v, x = y;
+      else r = l + (1 << v) - 2;
+    }
+  return l - n;
 }

tests/library_checker_aizu_tests/data_structures/simple_tree_inc_walk.test.cpp

@@ -1,6 +1,9 @@
 #define PROBLEM \
   "https://judge.yosupo.jp/problem/predecessor_problem"
 #include "../template.hpp"
+int __lg(unsigned x) {
+  return bit_width(x) - 1;
+}
 #include "../../../library/data_structures_[l,r]/seg_tree.hpp"
 int main() {
   cin.tie(0)->sync_with_stdio(0);
@@ -32,13 +35,8 @@ int main() {
       if (total == 0) {
         cout << -1 << '\n';
       } else {
-        int pref_sum = 0;
         cout << st.walk(0, k, [&](int sum) {
-          if (pref_sum + sum < total) {
-            pref_sum += sum;
-            return 1;
-          }
-          return 0;
+          return sum < total;
         }) << '\n';
       }
     }