There is an infinitely long street that runs west to east, which we consider as a number line.

There are N roadworks scheduled on this street. The i-th roadwork blocks the point at coordinate X_i from time S_i - 0.5 to time T_i - 0.5.

Q people are standing at coordinate 0. The i-th person will start the coordinate 0 at time D_i, continue to walk with speed 1 in the positive direction and stop walking when reaching a blocked point.

Find the distance each of the Q people will walk.

Constraints

* All values in input are integers.
* 1 \leq N, Q \leq 2 \times 10^5
* 0 \leq S_i < T_i \leq 10^9
* 1 \leq X_i \leq 10^9
* 0 \leq D_1 < D_2 < ... < D_Q \leq 10^9
* If i \neq j and X_i = X_j, the intervals [S_i, T_i) and [S_j, T_j) do not overlap.

Input

Input is given from Standard Input in the following format:


N Q
S_1 T_1 X_1
:
S_N T_N X_N
D_1
:
D_Q


Output

Print Q lines. The i-th line should contain the distance the i-th person will walk or -1 if that person walks forever.

Example

Input

4 6
1 3 2
7 13 10
18 20 13
3 4 2
0
1
2
3
5
8


Output

2
2
10
-1
13
-1
#include <iostream>
#include <cstdio>
#include <vector>
#include <algorithm>
#include <utility>
#include <string>
#include <tuple>
#include <set>

using namespace std;

using TUP = tuple<int, int, int>;
using PII = pair<int, int>;

int main() {
	int n, q, s, t, x, d;
	cin >> n >> q;

	vector<TUP> queries;
	for (int i = 0; i < n; i++) {
		cin >> s >> t >> x;

		queries.emplace_back(make_tuple(x, s, t));
	}
	sort(queries.begin(), queries.end());

	set<PII> ds;
	for (int i = 0; i < q; i++) {
		cin >> d;
		ds.insert(make_pair(d, i));
	}

	vector<int> ans(q, -1);
	for (auto query: queries) {
		tie(x, s, t) = query;
		// printf("query %3d %3d %3d: %3d %3d\n", x, s, t, s - x, t - x);

		auto it = ds.lower_bound(make_pair(s - x, 0));

		while (it != ds.end()) {
			if (it->first >= t - x) {
				break;
			}
			ans[it->second] = x;
			ds.erase(it++);
		}

	}

	for (auto z: ans) {
		cout << z << endl;
	}
	return 0;
}
