# CF1479D Odd Mineral Resource
## 题目描述
In Homer's country, there are $ n $ cities numbered $ 1 $ to $ n $ and they form a tree. That is, there are $ (n-1) $ undirected roads between these $ n $ cities and every two cities can reach each other through these roads.
Homer's country is an industrial country, and each of the $ n $ cities in it contains some mineral resource. The mineral resource of city $ i $ is labeled $ a_i $ .
Homer is given the plans of the country in the following $ q $ years. The plan of the $ i $ -th year is described by four parameters $ u_i, v_i, l_i $ and $ r_i $ , and he is asked to find any mineral resource $ c_i $ such that the following two conditions hold:
- mineral resource $ c_i $ appears an odd number of times between city $ u_i $ and city $ v_i $ ; and
- $ l_i \leq c_i \leq r_i $ .
As the best friend of Homer, he asks you for help. For every plan, find any such mineral resource $ c_i $ , or tell him that there doesn't exist one.
## 输入格式
The first line contains two integers $ n $ ( $ 1 \leq n \leq 3 \cdot 10^5 $ ) and $ q $ ( $ 1 \leq q \leq 3 \cdot 10^5 $ ), indicating the number of cities and the number of plans.
The second line contains $ n $ integers $ a_1, a_2, \dots, a_n $ ( $ 1 \leq a_i \leq n $ ).
Then the $ i $ -th line of the following $ (n-1) $ lines contains two integers $ x_i $ and $ y_i $ ( $ 1 \leq x_i, y_i \leq n $ ) with $ x_i \neq y_i $ , indicating that there is a bidirectional road between city $ x_i $ and city $ y_i $ . It is guaranteed that the given roads form a tree.
Then the $ i $ -th line of the following $ q $ lines contains four integers $ u_i $ , $ v_i $ , $ l_i $ , $ r_i $ ( $ 1 \leq u_i \leq n $ , $ 1 \leq v_i \leq n $ , $ 1 \leq l_i \leq r_i \leq n $ ), indicating the plan of the $ i $ -th year.
## 输出格式
Print $ q $ lines, the $ i $ -th of which contains an integer $ c_i $ such that
- $ c_i = {-1} $ if there is no such mineral resource that meets the required condition; or
- $ c_i $ is the label of the chosen mineral resource of the $ i $ -th year. The chosen mineral resource $ c_i $ should meet those conditions in the $ i $ -th year described above in the problem statement. If there are multiple choices of $ c_i $ , you can print any of them.
## 输入输出样例 #1
### 输入 #1
```
6 8
3 2 1 3 1 3
1 2
1 3
2 4
2 5
4 6
3 5 1 1
3 5 1 3
3 5 1 3
1 1 2 2
1 1 3 3
1 4 1 5
1 6 1 3
1 6 1 3
```
### 输出 #1
```
-1
2
3
-1
3
2
2
3
```
## 说明/提示
In the first three queries, there are four cities between city $ 3 $ and city $ 5 $ , which are city $ 1 $ , city $ 2 $ , city $ 3 $ and city $ 5 $ . The mineral resources appear in them are mineral resources $ 1 $ (appears in city $ 3 $ and city $ 5 $ ), $ 2 $ (appears in city $ 2 $ ) and $ 3 $ (appears in city $ 1 $ ). It is noted that
- The first query is only to check whether mineral source $ 1 $ appears an odd number of times between city $ 3 $ and city $ 5 $ . The answer is no, because mineral source $ 1 $ appears twice (an even number of times) between city $ 3 $ and city $ 5 $ .
- The second and the third queries are the same but they can choose different mineral resources. Both mineral resources $ 2 $ and $ 3 $ are available.
为什么WA了
```cpp
#include <bits/stdc++.h>
using namespace std;
const int BITS = 20;
const int MAX_N = 4e5 + 50;
const int BSIZE = 1;
int n, m, tot, a[MAX_N];
int fa[MAX_N][BITS], dep[MAX_N];
int dfn[MAX_N], in[MAX_N], out[MAX_N];
vector<int> e[MAX_N];
int L[MAX_N], R[MAX_N], pos[MAX_N];
int cnt[MAX_N], sum[MAX_N], ans[MAX_N];
struct Query {
int l, r, p, L, R, id;
bool operator < (const Query& rhs) const {
if (pos[l] != pos[rhs.l])
return pos[l] < pos[rhs.l];
return (pos[l] & 1) ? r < rhs.r : r > rhs.r;
}
} q[MAX_N];
void init() {
int cnt = n / BSIZE;
for (int i = 1; i <= cnt; i++) {
L[i] = (i - 1) * BSIZE + 1;
R[i] = i * BSIZE;
}
if (R[cnt] < n) {
L[cnt + 1] = R[cnt] + 1;
R[++cnt] = n;
}
for (int i = 1; i <= cnt; i++)
fill(pos + L[i], pos + R[i] + 1, i);
}
void modify(int idx) {
cout << "modify " << idx << '\n';
sum[pos[idx]] -= cnt[idx];
cnt[idx] ^= 1;
sum[pos[idx]] += cnt[idx];
}
int query(int lt, int rt) {
int lp = pos[lt], rp = pos[rt];
if (lp == rp) {
for (int i = lt; i <= rt; i++)
if (cnt[i])
return i;
} else {
for (int i = lt; i <= R[lp]; i++)
if (cnt[i])
return i;
for (int i = lp + 1; i < rp; i++)
if (sum[i])
for (int j = L[i]; j <= R[i]; j++)
if (cnt[j])
return j;
for (int i = L[rp]; i <= rt; i++)
if (cnt[i])
return i;
}
return -1;
}
void dfs(int u, int father, int depth) {
fa[u][0] = father, dep[u] = depth;
for (int k = 1; k < BITS; k++)
fa[u][k] = fa[fa[u][k - 1]][k - 1];
in[u] = ++tot, dfn[tot] = u;
for (int v : e[u])
if (v != father)
dfs(v, u, depth + 1);
out[u] = ++tot, dfn[tot] = u;
}
int LCA(int x, int y) {
if (dep[x] > dep[y])
swap(x, y);
for (int k = BITS - 1; ~k; k--)
if (dep[x] <= dep[fa[y][k]])
y = fa[y][k];
if (x == y)
return x;
for (int k = BITS - 1; ~k; k--)
if (fa[x][k] != fa[y][k])
x = fa[x][k], y = fa[y][k];
return x;
}
int main() {
cin >> n >> m;
for (int i = 1; i <= n; i++)
cin >> a[i];
for (int i = 1, u, v; i < n; i++) {
cin >> u >> v;
e[u].push_back(v);
e[v].push_back(u);
}
dfs(1, 0, 1);
for (int i = 1, u, v; i <= m; i++) {
cin >> u >> v >> q[i].L >> q[i].R;
q[i].id = i;
if (in[u] > in[v])
swap(u, v);
q[i].r = in[v];
int lca = LCA(u, v);
if (lca == u)
q[i].l = in[u], q[i].p = 0;
else
q[i].l = out[u], q[i].p = lca;
}
init();
sort(q + 1, q + m + 1);
int l = 1, r = 0;
for (int i = 1; i <= m; i++) {
int ql = q[i].l, qr = q[i].r;
while (l > ql)
modify(a[dfn[--l]]);
while (r < qr)
modify(a[dfn[++r]]);
while (l < ql)
modify(a[dfn[l++]]);
while (r > qr)
modify(a[dfn[r--]]);
if (q[i].p)
modify(a[q[i].p]);
cout << q[i].id << '\n';
ans[q[i].id] = query(q[i].L, q[i].R);
if (q[i].p)
modify(a[q[i].p]);
}
for (int i = 1; i <= n; i++)
cout << ans[i] << '\n';
return 0;
}
```
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