Merge remote-tracking branch 'origin/dev' into recursive-lambda-by-ref

# Conflicts:
#	.verify-helper/timestamps.remote.json

Author: Cameron Custer

.verify-helper/timestamps.remote.json

@@ -5,13 +5,13 @@
 "tests/library_checker_aizu_tests/convolution/xor_convolution.test.cpp": "2026-03-06 12:17:28 -0700",
 "tests/library_checker_aizu_tests/data_structures/binary_search_example.test.cpp": "2024-11-18 10:51:39 -0600",
 "tests/library_checker_aizu_tests/data_structures/binary_trie.test.cpp": "2026-01-18 02:20:40 +0000",
-"tests/library_checker_aizu_tests/data_structures/bit.test.cpp": "2026-04-26 11:38:07 -0600",
-"tests/library_checker_aizu_tests/data_structures/bit_inc.test.cpp": "2026-04-06 12:17:32 -0600",
-"tests/library_checker_aizu_tests/data_structures/bit_inc_walk.test.cpp": "2026-04-06 12:17:32 -0600",
-"tests/library_checker_aizu_tests/data_structures/bit_ordered_set.test.cpp": "2026-04-06 12:17:32 -0600",
-"tests/library_checker_aizu_tests/data_structures/bit_rupq.test.cpp": "2026-04-06 12:17:32 -0600",
-"tests/library_checker_aizu_tests/data_structures/bit_rurq.test.cpp": "2026-04-06 12:17:32 -0600",
-"tests/library_checker_aizu_tests/data_structures/bit_walk.test.cpp": "2026-04-26 11:38:07 -0600",
+"tests/library_checker_aizu_tests/data_structures/bit.test.cpp": "2026-07-06 09:26:00 -0700",
+"tests/library_checker_aizu_tests/data_structures/bit_inc.test.cpp": "2026-07-06 09:26:00 -0700",
+"tests/library_checker_aizu_tests/data_structures/bit_inc_walk.test.cpp": "2026-07-06 09:26:00 -0700",
+"tests/library_checker_aizu_tests/data_structures/bit_ordered_set.test.cpp": "2026-07-06 09:26:00 -0700",
+"tests/library_checker_aizu_tests/data_structures/bit_rupq.test.cpp": "2026-07-06 09:26:00 -0700",
+"tests/library_checker_aizu_tests/data_structures/bit_rurq.test.cpp": "2026-07-06 09:26:00 -0700",
+"tests/library_checker_aizu_tests/data_structures/bit_walk.test.cpp": "2026-07-06 09:26:00 -0700",
 "tests/library_checker_aizu_tests/data_structures/deque.test.cpp": "2026-01-18 02:20:40 +0000",
 "tests/library_checker_aizu_tests/data_structures/deque_index.test.cpp": "2026-01-18 02:20:40 +0000",
 "tests/library_checker_aizu_tests/data_structures/deque_op.test.cpp": "2026-01-18 02:20:40 +0000",
@@ -33,7 +33,7 @@
 "tests/library_checker_aizu_tests/data_structures/permutation_tree.test.cpp": "2026-05-24 23:00:07 -0500",
 "tests/library_checker_aizu_tests/data_structures/persistent_queue_tree.test.cpp": "2026-04-26 11:38:07 -0600",
 "tests/library_checker_aizu_tests/data_structures/persistent_seg_tree.test.cpp": "2026-04-26 11:38:07 -0600",
-"tests/library_checker_aizu_tests/data_structures/pq_ds_undo_sliding_window.test.cpp": "2026-01-18 02:20:40 +0000",
+"tests/library_checker_aizu_tests/data_structures/pq_ds_undo_sliding_window.test.cpp": "2026-07-06 09:26:00 -0700",
 "tests/library_checker_aizu_tests/data_structures/rmq_linear.test.cpp": "2026-05-24 23:00:07 -0500",
 "tests/library_checker_aizu_tests/data_structures/rmq_sparse_table.test.cpp": "2026-05-24 23:00:07 -0500",
 "tests/library_checker_aizu_tests/data_structures/rmq_sparse_table_inc.test.cpp": "2026-01-18 11:15:41 +0000",
@@ -90,7 +90,7 @@
 "tests/library_checker_aizu_tests/handmade_tests/permutation_tree_small.test.cpp": "2026-05-24 23:00:07 -0500",
 "tests/library_checker_aizu_tests/handmade_tests/rmq_small_n.test.cpp": "2026-05-24 23:00:07 -0500",
 "tests/library_checker_aizu_tests/handmade_tests/sa_find_subarray.test.cpp": "2026-04-26 11:38:07 -0600",
-"tests/library_checker_aizu_tests/handmade_tests/seg_tree_find.test.cpp": "2026-04-26 11:38:07 -0600",
+"tests/library_checker_aizu_tests/handmade_tests/seg_tree_find.test.cpp": "2026-07-06 09:26:00 -0700",
 "tests/library_checker_aizu_tests/handmade_tests/seg_tree_find_small.test.cpp": "2026-04-26 11:38:07 -0600",
 "tests/library_checker_aizu_tests/handmade_tests/seg_tree_midpoint.test.cpp": "2026-04-26 11:38:07 -0600",
 "tests/library_checker_aizu_tests/handmade_tests/xor_basis_walk.test.cpp": "2026-03-08 15:33:28 -0600",
@@ -108,7 +108,7 @@
 "tests/library_checker_aizu_tests/math/partitions.test.cpp": "2025-08-28 13:19:16 -0600",
 "tests/library_checker_aizu_tests/math/prime_sieve.test.cpp": "2024-11-22 11:54:52 -0600",
 "tests/library_checker_aizu_tests/math/solve_linear_mod.test.cpp": "2026-04-12 10:51:29 -0600",
-"tests/library_checker_aizu_tests/math/tetration.test.cpp": "2024-11-17 14:04:03 -0600",
+"tests/library_checker_aizu_tests/math/tetration.test.cpp": "2026-07-06 09:26:00 -0700",
 "tests/library_checker_aizu_tests/math/totient.test.cpp": "2024-11-17 14:04:03 -0600",
 "tests/library_checker_aizu_tests/math/xor_basis_intersection.test.cpp": "2026-04-26 11:38:07 -0600",
 "tests/library_checker_aizu_tests/monotonic_stack_related/cartesian_binary_tree.test.cpp": "2026-04-06 13:24:49 -0600",
@@ -120,7 +120,7 @@
 "tests/library_checker_aizu_tests/strings/lcp_query_palindrome.test.cpp": "2026-04-26 11:38:07 -0600",
 "tests/library_checker_aizu_tests/strings/lcp_query_zfunc.test.cpp": "2026-04-26 11:38:07 -0600",
 "tests/library_checker_aizu_tests/strings/lcs_dp.test.cpp": "2025-08-05 19:19:23 -0600",
-"tests/library_checker_aizu_tests/strings/lcs_queries.test.cpp": "2026-04-06 12:17:32 -0600",
+"tests/library_checker_aizu_tests/strings/lcs_queries.test.cpp": "2026-07-06 09:26:00 -0700",
 "tests/library_checker_aizu_tests/strings/lcs_queries_merge_sort_tree.test.cpp": "2026-04-26 11:38:07 -0600",
 "tests/library_checker_aizu_tests/strings/manacher.test.cpp": "2026-04-26 11:38:07 -0600",
 "tests/library_checker_aizu_tests/strings/multi_matching_bs.test.cpp": "2026-04-26 11:38:07 -0600",
@@ -137,11 +137,11 @@
 "tests/library_checker_aizu_tests/trees/edge_cd_contour_range_update.test.cpp": "2026-07-06 09:57:36 -0700",
 "tests/library_checker_aizu_tests/trees/edge_cd_count_paths_per_length.test.cpp": "2026-07-06 09:57:36 -0700",
 "tests/library_checker_aizu_tests/trees/edge_cd_reroot_dp.test.cpp": "2026-07-06 09:57:36 -0700",
-"tests/library_checker_aizu_tests/trees/hld_aizu1.test.cpp": "2026-04-12 16:21:27 -0600",
+"tests/library_checker_aizu_tests/trees/hld_aizu1.test.cpp": "2026-07-06 09:26:00 -0700",
 "tests/library_checker_aizu_tests/trees/hld_aizu2.test.cpp": "2026-04-26 11:38:07 -0600",
-"tests/library_checker_aizu_tests/trees/hld_lib_checker_path.test.cpp": "2026-04-12 16:21:27 -0600",
-"tests/library_checker_aizu_tests/trees/hld_lib_checker_subtree_edges.test.cpp": "2026-04-12 16:21:27 -0600",
-"tests/library_checker_aizu_tests/trees/hld_lib_checker_subtree_nodes.test.cpp": "2026-04-12 16:21:27 -0600",
+"tests/library_checker_aizu_tests/trees/hld_lib_checker_path.test.cpp": "2026-07-06 09:26:00 -0700",
+"tests/library_checker_aizu_tests/trees/hld_lib_checker_subtree_edges.test.cpp": "2026-07-06 09:26:00 -0700",
+"tests/library_checker_aizu_tests/trees/hld_lib_checker_subtree_nodes.test.cpp": "2026-07-06 09:26:00 -0700",
 "tests/library_checker_aizu_tests/trees/kth_path_hagerup.test.cpp": "2026-07-06 09:57:36 -0700",
 "tests/library_checker_aizu_tests/trees/kth_path_ladder.test.cpp": "2026-07-06 09:57:36 -0700",
 "tests/library_checker_aizu_tests/trees/kth_path_linear.test.cpp": "2026-07-06 09:57:36 -0700",

library/contest/README.md

@@ -9,7 +9,7 @@ freopen("output.txt", "w", stdout);
 If you changed something for debugging, add a `cout << "don't submit" << endl;`
 or `assert(0);` at the end of the code
 
-for policy base DS:
+for policy-based DS:
 ```
 #include <bits/extc++.h>
 ```
@@ -25,7 +25,7 @@ don't use cin for doubles/floats, it's slow, read into string, then convert to d
 cin.exceptions(cin.failbit);
 ```
 
-- use pramgas for C++ speed boost
+- use pragmas for C++ speed boost
 ```
 #pragma GCC optimize("O3,unroll-loops")
 #pragma GCC target("avx2,bmi,bmi2,lzcnt,popcnt")

library/data_structures_[l,r)/bit.hpp

@@ -7,6 +7,7 @@
 //!   int r = bit.walk2(sum);
 //!   // Returns min r s.t. sum of [0,r] >= sum
 //!   // Returns n if sum of [0,n-1] < sum
+//!   // Returns -1 if sum <= 0
 //! @endcode
 //! @time O(n + q log n)
 //! @space O(n)

library/data_structures_[l,r)/uncommon/priority_queue_of_updates.hpp

@@ -1,13 +1,12 @@
 #pragma once
 //! https://codeforces.com/blog/entry/111117
 //! @code
-//!     dsu_restorable dsu_r(n);
-//!     pq_updates<dsu_restorable, int, int> pq(dsu_r);
-//!     rep (i, 0, n) pq.ds.add(i, initial_nums[i]);
-//!     //or
-//!     pq.ds.subtree = initial_nums;
-//!     pq.push_update(u, v, curr_pri);
-//!     cout << pq.ds.sum(v) << '\n';
+//!   // DS = any struct with member functions join, undo
+//!   DS ds;
+//!   // int = argument type of DS::join
+//!   pq_updates<DS, int> pq(ds);
+//!   pq.push_update(val, priority);
+//!   pq.pop_update();
 //! @endcode
 //! @time n interweaved calls to pop_update, push_update
 //! take O(T(n)*nlogn) where O(T(n)) = time complexity of

library/data_structures_[l,r]/bit.hpp

@@ -7,6 +7,7 @@
 //!   int r = bit.walk2(sum);
 //!   // Returns min r s.t. sum of [0,r] >= sum
 //!   // Returns n if sum of [0,n-1] < sum
+//!   // Returns -1 if sum <= 0
 //! @endcode
 //! @time O(n + q log n)
 //! @space O(n)

library/graphs/uncommon/block_vertex_tree.hpp

@@ -15,7 +15,7 @@
 //! [0, n) are original nodes
 //! [n, n + num_bccs) are BCC nodes
 //! @time O(n + m)
-//! @time O(n)
+//! @space O(n)
 auto block_vertex_tree(const auto& g, int num_bccs,
   const vi& bcc_id) {
   int n = sz(g);

library/math/tetration_mod.hpp

@@ -7,7 +7,7 @@
 //!
 //! returns b ^ (b ^ (... ^ b))) % mod, where
 //!   the height of the tower is e.
-//
+//!
 //! @time O(sqrt(mod) * log(mod))
 //! @space O(log(mod))
 ll bin_exp(ll b, ll e, int mod) {