• 区間の端点で分割して座圧っぽく$O(Q^2\log Q)$ $\to$ TLE
• 使い終わって区間を併合すれば $\to$ 焼け石に水
• (ここで解説を見た)
• bucketのindexのあたりのミス $\to$ WA
• int bucket_size = ceil(sqrt(query)); $\to$ TLE

## implementation

#include <cstdio>
#include <vector>
#include <cmath>
#include <queue>
#define repeat(i,n) for (int i = 0; (i) < int(n); ++(i))
#define repeat_from(i,m,n) for (int i = (m); (i) < int(n); ++(i))
using namespace std;
int main() {
// input
int n, query; scanf("%d%d", &n, &query);
vector<int> x(n); repeat (i,n) scanf("%d", &x[i]);
// square root decomposition
int bucket_size = ceil(sqrt(n));
int bucket_count = ceil(n /(double) bucket_size);
vector<priority_queue<int> > bucket(bucket_count);
vector<priority_queue<int> > bucket_query(bucket_count);
auto flush = [&](int i) { // move bucket_query -> x
if (bucket_query[i].empty()) return;
int l = i * bucket_size;
int r = min(n, (i+1) * bucket_size);
repeat_from (j,l,r) {
int value = - bucket_query[i].top();
if (value < x[j]) {
bucket_query[i].pop();
bucket_query[i].push(- x[j]);
x[j] = value;
}
}
bucket_query[i] = priority_queue<int>();
};
auto reset = [&](int i) { // move x -> bucket
int l = i * bucket_size;
int r = min(n, (i+1) * bucket_size);
bucket[i] = priority_queue<int>();
repeat_from (j,l,r) {
bucket[i].push(x[j]);
}
};
// init
repeat (i,bucket_count) {
reset(i);
}
// run
auto func = [&](int l, int r, int p) {
int i = l / bucket_size;
if (l % bucket_size != 0) {
flush(i);
int limit = min(r, (i+1) * bucket_size);
for (; l < limit; ++ l) if (p < x[l]) swap(p, x[l]);
reset(i);
++ i;
}
for (; l + bucket_size - 1 < r; l += bucket_size, ++ i) {
int value = bucket[i].top();
if (p < value) {
bucket_query[i].push(- p);
bucket[i].pop();
bucket[i].push(p);
p = value;
}
}
if (l != r) {
flush(i);
for (; l < r; ++ l) if (p < x[l]) swap(p, x[l]);
reset(i);
}
return p;
};
while (query --) {
int l, r, p; scanf("%d%d%d", &l, &r, &p); -- l;
if (l < r) {
p = func(l, r, p);
} else {
p = func(l, n, p);
p = func(0, r, p);
}
// output
printf("%d\n", p);
}
return 0;
}