Yet Another Array Queries Problem

You are given an array a of size n, and q queries to it. There are queries of two types:

• 1 l _i r _i — perform a cyclic shift of the segment [l _i, r _i] to the right. That is, for every x such that l _i ≤ x < r _i new value of a _x + 1 becomes equal to old value of a _x, and new value of a _l i becomes equal to old value of a _r i;
• 2 l _i r _i — reverse the segment [l _i, r _i].

There are m important indices in the array b ₁, b ₂, …, b _m. For each i such that 1 ≤ i ≤ m you have to output the number that will have index b _i in the array after all queries are performed.

Input

The first line contains three integer numbers n, q and m (1 ≤ n, q ≤ 2·10⁵, 1 ≤ m ≤ 100).

The second line contains n integer numbers a ₁, a ₂, …, a _n (1 ≤ a _i ≤ 10⁹).

Then q lines follow. i-th of them contains three integer numbers t _i, l _i, r _i, where t _i is the type of i-th query, and [l _i, r _i] is the segment where this query is performed (1 ≤ t _i ≤ 2, 1 ≤ l _i ≤ r _i ≤ n).

The last line contains m integer numbers b ₁, b ₂, …, b _m (1 ≤ b _i ≤ n) — important indices of the array.

Output

Print m numbers, i-th of which is equal to the number at index b _i after all queries are done.

Example

input

6 3 5
1 2 3 4 5 6
2 1 3
2 3 6
1 1 6
2 2 1 5 3

output

3 3 1 5 2 

Solution:

#include <bits/stdc++.h>

using namespace std;

mt19937 rng((unsigned int) chrono::steady_clock::now().time_since_epoch().count());

class node {
public:
int id;
node* l;
node* r;
node* p;
bool rev;
int sz;
// declare extra variables:
int P;

node(int _id) {
id = _id;
l = r = p = NULL;
rev = false;
sz = 1;
// init extra variables:
P = rng();
}

void unsafe_reverse() {
rev ^= 1;
swap(l, r);
pull();
}

// apply changes:
void unsafe_apply() {

}

void push() {
if (rev) {
if (l != NULL) {
l->unsafe_reverse();
}
if (r != NULL) {
r->unsafe_reverse();
}
rev = 0;
}
// now push everything else:

}

void pull() {
sz = 1;
// now init from self:

if (l != NULL) {
l->p = this;
sz += l->sz;
// now pull from l:

}
if (r != NULL) {
r->p = this;
sz += r->sz;
// now pull from r:

}
}
};

void debug_node(node* v, string pref = "") {
#ifdef LOCAL
if (v != NULL) {
debug_node(v->r, pref + " ");
cerr << pref << "-" << " " << v->id << '\n';
      debug_node(v->l, pref + " ");
} else {
cerr << pref << "-" << " " << "NULL" << '\n';
    }
  #endif
}

namespace treap {
  pair<node*,int> find(node* v, const function<int(node*)> &go_to) {
// go_to returns: 0 -- found; -1 -- go left; 1 -- go right
// find returns the last vertex on the descent and its go_to
if (v == NULL) {
return {NULL, 0};
}
int dir;
while (true) {
v->push();
dir = go_to(v);
if (dir == 0) {
break;
}
node* u = (dir == -1 ? v->l : v->r);
if (u == NULL) {
break;
}
v = u;
}
return {v, dir};
}

node* get_leftmost(node* v) {
return find(v, [&](node*) { return -1; }).first;
}

node* get_rightmost(node* v) {
return find(v, [&](node*) { return 1; }).first;
}

node* get_kth(node* v, int k) { // 0-indexed
pair<node*,int> p = find(v, [&](node* u) {
if (u->l != NULL) {
if (u->l->sz > k) {
return -1;
}
k -= u->l->sz;
}
if (k == 0) {
return 0;
}
k--;
return 1;
});
return (p.second == 0 ? p.first : NULL);
}

int get_position(node* v) { // 0-indexed
int k = (v->l != NULL ? v->l->sz : 0);
while (v->p != NULL) {
if (v == v->p->r) {
k++;
if (v->p->l != NULL) {
k += v->p->l->sz;
}
}
v = v->p;
}
return k;
}

node* get_bst_root(node* v) {
while (v->p != NULL) {
v = v->p;
}
return v;
}

pair<node*,node*> split(node* v, const function<bool(node*)> &is_right) {
if (v == NULL) {
return {NULL, NULL};
}
v->push();
if (is_right(v)) {
pair<node*,node*> p = split(v->l, is_right);
if (p.first != NULL) {
p.first->p = NULL;
}
v->l = p.second;
v->pull();
return {p.first, v};
} else {
pair<node*,node*> p = split(v->r, is_right);
v->r = p.first;
if (p.second != NULL) {
p.second->p = NULL;
}
v->pull();
return {v, p.second};
}
}

pair<node*,node*> split_leftmost_k(node* v, int k) {
return split(v, [&](node* u) {
int left_and_me = (u->l != NULL ? u->l->sz : 0) + 1;
if (k >= left_and_me) {
k -= left_and_me;
return false;
}
return true;
});
}

node* merge(node* v, node* u) {
if (v == NULL) {
return u;
}
if (u == NULL) {
return v;
}
if (v->P > u->P) {
//    if (rng() % (v->sz + u->sz) < (unsigned int) v->sz) {
v->push();
v->r = merge(v->r, u);
v->pull();
return v;
} else {
u->push();
u->l = merge(v, u->l);
u->pull();
return u;
}
}

node* add(node* r, node* v, const function<bool(node*)> &go_left) {
pair<node*,node*> p = split(r, go_left);
return merge(p.first, merge(v, p.second));
}

node* remove(node* v) { // returns the new root
v->push();
node* x = v->l;
node* y = v->r;
node* p = v->p;
v->l = v->r = v->p = NULL;
v->push();
v->pull(); // now v might be reusable...
node* z = merge(x, y);
if (p == NULL) {
if (z != NULL) {
z->p = NULL;
}
return z;
}
if (p->l == v) {
p->l = z;
}
if (p->r == v) {
p->r = z;
}
while (true) {
p->push();
p->pull();
if (p->p == NULL) {
break;
}
p = p->p;
}
return p;
}

node* next(node* v) {
if (v->r == NULL) {
while (v->p != NULL && v->p->r == v) {
v = v->p;
}
return v->p;
}
v->push();
v = v->r;
while (v->l != NULL) {
v->push();
v = v->l;
}
return v;
}

node* prev(node* v) {
if (v->l == NULL) {
while (v->p != NULL && v->p->l == v) {
v = v->p;
}
return v->p;
}
v->push();
v = v->l;
while (v->r != NULL) {
v->push();
v = v->r;
}
return v;
}

int get_size(node* v) {
return (v != NULL ? v->sz : 0);
}

template<typename... T>
void apply(node* v, T... args) {
v->unsafe_apply(args...);
}

void reverse(node* v) {
v->unsafe_reverse();
}
}

using namespace treap;

int main() {
ios::sync_with_stdio(false);
cin.tie(0);
int n, qq, m;
cin >> n >> qq >> m;
vector<int> a(n);
for (int i = 0; i < n; i++) {
    cin >> a[i];
}
node* r = NULL;
for (int i = 0; i < n; i++) {
    r = merge(r, new node(i));
  }
  while (qq--) {
    int op, x, y;
    cin >> op >> x >> y;
x--; y--;
if (op == 1) {
pair<node*,node*> p = split_leftmost_k(r, x);
pair<node*,node*> q = split_leftmost_k(p.second, y - x);
pair<node*,node*> t = split_leftmost_k(q.second, 1);
r = merge(p.first, merge(t.first, merge(q.first, t.second)));
} else {
pair<node*,node*> p = split_leftmost_k(r, x);
pair<node*,node*> q = split_leftmost_k(p.second, y - x + 1);
reverse(q.first);
r = merge(p.first, merge(q.first, q.second));
}
}
for (int i = 0; i < m; i++) {
    if (i > 0) {
cout << " ";
    }
    int foo;
    cin >> foo;
foo--;
node* v = get_kth(r, foo);
assert(v != NULL);
cout << a[v->id];
}
cout << '\n';
  return 0;
}