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 <bits/stdc++.h>
using i64 = long long;

int main() {
    int n, q;
    std::cin >> n >> q;
    std::vector<std::pair<int, std::pair<int, int>>> v;
    for (int i = 0; i < n; i++) {
        int a, b, c;
        std::cin >> a >> b >> c;
        v.push_back({ c, { a - c, b - c } });
    }
    std::sort(v.begin(), v.end());
    std::set<std::pair<int, int>> d;
    for (int i = 0; i < q; i++) {
        int in;
        std::cin >> in;
        d.emplace(in, i);
    }
    std::vector<int> ret(q, -1);
    for (int i = 0; i < n; i++) {
        auto it = d.lower_bound(std::make_pair(v[i].second.first, 0));
        while (it != d.end() && it->first < v[i].second.second) {
            ret[it->second] = v[i].first;
            it = d.erase(it);
        }
    }
    for (const auto e : ret) std::cout << e << std::endl;

    return 0;
}
