diff --git a/.verify-helper/timestamps.remote.json b/.verify-helper/timestamps.remote.json
index cf01aa5f..d69f62e4 100644
--- a/.verify-helper/timestamps.remote.json
+++ b/.verify-helper/timestamps.remote.json
@@ -144,6 +144,7 @@
 "tests/library_checker_aizu_tests/trees/kth_path_tree_lift.test.cpp": "2025-08-14 10:27:46 -0600",
 "tests/library_checker_aizu_tests/trees/lca_all_methods_aizu.test.cpp": "2025-08-21 12:17:27 -0600",
 "tests/library_checker_aizu_tests/trees/lca_all_methods_lib_checker.test.cpp": "2025-08-21 12:17:27 -0600",
-"tests/library_checker_aizu_tests/trees/shallowest_aizu_tree_height.test.cpp": "2025-08-30 00:58:07 -0600",
+"tests/library_checker_aizu_tests/trees/shallowest_aizu_tree_height.test.cpp": "2025-09-03 10:28:33 -0600",
+"tests/library_checker_aizu_tests/trees/shallowest_lib_checker_tree_path_composite.test.cpp": "2025-09-03 10:28:33 -0600",
 "tests/library_checker_aizu_tests/trees/subtree_isomorphism.test.cpp": "2025-08-14 10:27:46 -0600"
 }
\ No newline at end of file
diff --git a/library/trees/shallowest_decomp_tree.hpp b/library/trees/shallowest_decomp_tree.hpp
index 7509491f..8256982c 100644
--- a/library/trees/shallowest_decomp_tree.hpp
+++ b/library/trees/shallowest_decomp_tree.hpp
@@ -21,7 +21,7 @@ void shallowest(auto& adj, auto f) {
     return dp;
   };
   dfs(dfs, 0, 0);
-  for (vi vec : order | views::reverse)
+  for (const vi& vec : order | views::reverse)
     for (int v : vec) {
       f(v);
       for (int u : adj[v])
diff --git a/tests/library_checker_aizu_tests/trees/shallowest_lib_checker_tree_path_composite.test.cpp b/tests/library_checker_aizu_tests/trees/shallowest_lib_checker_tree_path_composite.test.cpp
new file mode 100644
index 00000000..6c115054
--- /dev/null
+++ b/tests/library_checker_aizu_tests/trees/shallowest_lib_checker_tree_path_composite.test.cpp
@@ -0,0 +1,93 @@
+#define PROBLEM \
+  "https://judge.yosupo.jp/problem/tree_path_composite_sum"
+#undef _GLIBCXX_DEBUG
+#include "../template.hpp"
+#include "../../../library/trees/shallowest_decomp_tree.hpp"
+#include "../../../library/math/mod_int.hpp"
+using line = array<mint, 2>;
+// returns f(g(x)) = f[0]*(g[0]*x+g[1]) + f[1]
+line compose(line f, line g) {
+  return {f[0] * g[0], f[1] + f[0] * g[1]};
+}
+int main() {
+  cin.tie(0)->sync_with_stdio(0);
+  int n;
+  cin >> n;
+  vector<mint> a(n);
+  for (int i = 0; i < n; i++) cin >> a[i].x;
+  vector<vector<int>> adj(n);
+  vector<vector<line>> weight(n);
+  for (int i = 0; i < n - 1; i++) {
+    int u, v, b, c;
+    cin >> u >> v >> b >> c;
+    adj[u].push_back(v);
+    adj[v].push_back(u);
+    weight[u].push_back({b, c});
+    weight[v].push_back({b, c});
+  }
+  vector<mint> res(n);
+  for (int i = 0; i < n; i++) res[i] = a[i];
+  shallowest(adj, [&](int cent) {
+    assert(ssize(adj[cent]) == ssize(weight[cent]));
+    mint total_sum_evaluated = 0;
+    int total_cnt_nodes = 0;
+    mint curr_sum_evaluated = 0;
+    int curr_cnt_nodes = 0;
+    auto dfs = [&](auto&& self, int v, int p,
+                 line downwards, line upwards,
+                 bool forwards) -> void {
+      // f(x) + f(y) + f(z) = b*x+c + b*y+c + b*z+c =
+      // b*(x+y+z) + c*3
+      res[v] = res[v] + upwards[0] * total_sum_evaluated +
+        upwards[1] * total_cnt_nodes;
+      if (forwards) {
+        res[v] =
+          res[v] + upwards[0] * a[cent] + upwards[1];
+        res[cent] =
+          res[cent] + downwards[0] * a[v] + downwards[1];
+      }
+      curr_cnt_nodes++;
+      curr_sum_evaluated = curr_sum_evaluated +
+        downwards[0] * a[v] + downwards[1];
+      for (int i = 0; i < ssize(adj[v]); i++) {
+        int u = adj[v][i];
+        line curr_line = weight[v][i];
+        if (u != p) {
+          self(self, u, v, compose(downwards, curr_line),
+            compose(curr_line, upwards), forwards);
+        }
+      }
+    };
+    for (int i = 0; i < ssize(adj[cent]); i++) {
+      curr_sum_evaluated = 0;
+      curr_cnt_nodes = 0;
+      dfs(dfs, adj[cent][i], cent, weight[cent][i],
+        weight[cent][i], 1);
+      total_sum_evaluated =
+        total_sum_evaluated + curr_sum_evaluated;
+      total_cnt_nodes += curr_cnt_nodes;
+    }
+    total_sum_evaluated = 0;
+    total_cnt_nodes = 0;
+    for (int i = ssize(adj[cent]) - 1; i >= 0; i--) {
+      curr_sum_evaluated = 0;
+      curr_cnt_nodes = 0;
+      dfs(dfs, adj[cent][i], cent, weight[cent][i],
+        weight[cent][i], 0);
+      total_sum_evaluated =
+        total_sum_evaluated + curr_sum_evaluated;
+      total_cnt_nodes += curr_cnt_nodes;
+    }
+    for (int v : adj[cent]) {
+      for (int i = 0; i < ssize(adj[v]); i++) {
+        if (adj[v][i] == cent) {
+          swap(weight[v][i], weight[v].back());
+          weight[v].pop_back();
+          break;
+        }
+      }
+    }
+  });
+  for (int i = 0; i < n; i++) cout << res[i].x << ' ';
+  cout << '\n';
+}