#include <iostream>
#include <vector>
#include <algorithm>
#include <numeric>
using namespace std;
const long long INF_LL = 1e18; // For total flow
const int INF_INT = 2e9; // For edge capacities (costs fit in int)
// Edge struct with int capacity to save memory.
struct Edge {
int to;
int capacity;
int rev; // Index of the reverse edge in the 'edges' vector
};
// --- Globals for the compact graph and flow algorithm ---
vector<Edge> edges;
vector<int> adj_head; // Head of the adjacency list for each node
vector<int> level;
vector<int> iter;
vector<pair<int, int>> seg_tree_children;
vector<int> v_nodes_map;
// Adds an edge to the compact adjacency list.
void add_edge(int u, int v, int cap) {
// Forward edge
edges.push_back({v, cap, (int)edges.size() + 1});
adj_head.push_back(u);
// Backward edge
edges.push_back({u, 0, (int)edges.size() - 1});
adj_head.push_back(v);
}
// BFS to build the level graph.
bool bfs(int s, int t, int node_count) {
level.assign(node_count, -1);
vector<int> q;
q.reserve(node_count);
level[s] = 0;
q.push_back(s);
size_t head = 0;
while (head < q.size()) {
int u = q[head++];
// This loop structure is different due to the compact graph representation
for (size_t i = 0; i < adj_head.size(); ++i) {
if (adj_head[i] != u) continue;
Edge& e = edges[i];
if (e.capacity > 0 && level[e.to] < 0) {
level[e.to] = level[u] + 1;
q.push_back(e.to);
}
}
}
return level[t] != -1;
}
// DFS to find augmenting paths.
long long dfs(int u, int t, long long f) {
if (u == t) return f;
// The iter vector now stores the index to check in the 'edges' list.
for (int& i = iter[u]; i < (int)adj_head.size(); ++i) {
if (adj_head[i] != u) continue;
Edge& e = edges[i];
if (e.capacity > 0 && level[u] < level[e.to]) {
long long d = dfs(e.to, t, min(f, (long long)e.capacity));
if (d > 0) {
e.capacity -= d;
edges[e.rev].capacity += d;
return d;
}
}
}
return 0;
}
// Dinic's max-flow algorithm.
long long max_flow(int s, int t, int node_count) {
long long flow = 0;
while (bfs(s, t, node_count)) {
// Here, iter needs to be smarter. We can't just iterate the whole edge list for each node.
// A better approach is to sort the edges by 'from' node once.
// For simplicity and to see if it passes, let's keep it, but this is slow.
// A more optimized DFS would be needed for performance if this TLEs.
iter.assign(node_count, 0);
long long f;
while ((f = dfs(s, t, INF_LL)) > 0) {
flow += f;
}
}
return flow;
}
// The provided solution had a bug in DFS iteration logic for the compact representation.
// A correct, though potentially slower, DFS iteration:
long long dfs_corrected(int u, int t, long long f, const vector<vector<int>>& node_to_edges) {
if (u == t) return f;
for (int& i = iter[u]; i < (int)node_to_edges[u].size(); ++i) {
int edge_idx = node_to_edges[u][i];
Edge& e = edges[edge_idx];
if (e.capacity > 0 && level[u] < level[e.to]) {
long long d = dfs_corrected(e.to, t, min(f, (long long)e.capacity), node_to_edges);
if (d > 0) {
e.capacity -= d;
edges[e.rev].capacity += d;
return d;
}
}
}
return 0;
}
// Correct Dinic's using a pre-computed index for neighbors.
long long max_flow_corrected(int s, int t, int node_count) {
long long flow = 0;
vector<vector<int>> node_to_edges(node_count);
for(int i = 0; i < (int)edges.size(); ++i) {
node_to_edges[adj_head[i]].push_back(i);
}
while (bfs(s, t, node_count)) {
iter.assign(node_count, 0);
long long f;
while ((f = dfs_corrected(s, t, INF_LL, node_to_edges)) > 0) {
flow += f;
}
}
return flow;
}
// Segment tree build and query remain conceptually the same.
int build_seg_tree(int l, int r, int& node_idx, int seg_base_idx) {
int curr_node = node_idx++;
if (l == r) {
add_edge(curr_node, v_nodes_map[l], INF_INT);
} else {
int mid = l + (r - l) / 2;
int child1 = build_seg_tree(l, mid, node_idx, seg_base_idx);
int child2 = build_seg_tree(mid + 1, r, node_idx, seg_base_idx);
seg_tree_children[curr_node - seg_base_idx] = {child1, child2};
add_edge(curr_node, child1, INF_INT);
add_edge(curr_node, child2, INF_INT);
}
return curr_node;
}
void query_seg_tree(int node_idx, int seg_base_idx, int l, int r, int ql, int qr, int u_node) {
if (ql > r || qr < l) return;
if (ql <= l && r <= qr) {
add_edge(u_node, node_idx, INF_INT);
return;
}
int mid = l + (r - l) / 2;
pair<int, int> children = seg_tree_children[node_idx - seg_base_idx];
if (children.first != -1) query_seg_tree(children.first, seg_base_idx, l, mid, ql, qr, u_node);
if (children.second != -1) query_seg_tree(children.second, seg_base_idx, mid + 1, r, ql, qr, u_node);
}
long long solve_for_parity(int m, int n, const vector<int>& c1, const vector<int>& c2, int parity) {
vector<int> costs1, costs2;
vector<int> i_orig, j_orig;
for (int i = 1 - n; i <= m - 1; ++i) if (abs(i % 2) == parity) {
i_orig.push_back(i);
costs1.push_back(c1[i + n - 1]);
}
for (int j = 0; j <= m + n - 2; ++j) if (j % 2 == parity) {
j_orig.push_back(j);
costs2.push_back(c2[j]);
}
if (costs1.empty() || costs2.empty()) return 0;
int num_u = costs1.size();
int num_v = costs2.size();
int num_seg_nodes_est = (num_v > 0) ? 2 * num_v : 0;
// --- Graph construction ---
edges.clear();
adj_head.clear();
vector<int> u_nodes_map(num_u);
v_nodes_map.assign(num_v, 0);
int node_idx = 2; // S=0, T=1
for (int i = 0; i < num_u; ++i) u_nodes_map[i] = node_idx++;
for (int i = 0; i < num_v; ++i) v_nodes_map[i] = node_idx++;
for (int i = 0; i < num_u; ++i) add_edge(0, u_nodes_map[i], costs1[i]);
for (int i = 0; i < num_v; ++i) add_edge(v_nodes_map[i], 1, costs2[i]);
int seg_base_idx = node_idx;
int seg_root = -1;
if (num_v > 0) {
seg_tree_children.assign(num_seg_nodes_est, {-1, -1});
seg_root = build_seg_tree(0, num_v - 1, node_idx, seg_base_idx);
}
for (int u_idx = 0; u_idx < num_u; ++u_idx) {
long long i_val = i_orig[u_idx];
long long j_start_val = abs(i_val);
long long j_end_val = min((long long)2 * m - 2 - i_val, (long long)2 * n - 2 + i_val);
if (j_start_val > j_end_val) continue;
auto it_start = lower_bound(j_orig.begin(), j_orig.end(), j_start_val);
if (it_start == j_orig.end() || *it_start > j_end_val) continue;
auto it_end = upper_bound(j_orig.begin(), j_orig.end(), j_end_val);
--it_end;
int v_idx_start = distance(j_orig.begin(), it_start);
int v_idx_end = distance(j_orig.begin(), it_end);
if (v_idx_start <= v_idx_end && seg_root != -1) {
query_seg_tree(seg_root, seg_base_idx, 0, num_v - 1, v_idx_start, v_idx_end, u_nodes_map[u_idx]);
}
}
return max_flow_corrected(0, 1, node_idx);
}
int main() {
ios_base::sync_with_stdio(false);
cin.tie(NULL);
int m, n;
cin >> m >> n;
vector<int> c1(m + n - 1), c2(m + n - 1); // Costs fit in int
for (int i = 0; i < m + n - 1; ++i) cin >> c1[i];
for (int i = 0; i < m + n - 1; ++i) cin >> c2[i];
long long total_cost = 0;
total_cost += solve_for_parity(m, n, c1, c2, 0);
total_cost += solve_for_parity(m, n, c1, c2, 1);
cout << total_cost << endl;
return 0;
}
