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 namespace std;
typedef pair<int, int> pii;

int n, q;

struct node {
    int time, corr, kind;
    bool operator<(const node &p) const {
        return time < p.time;
    }
};

int main() {
    ios_base::sync_with_stdio(0); cin.tie(0);
    cin >> n >> q;
    vector<node> v;
    for (int i = 0; i < n; i++) {
        int s, t, x;
        cin >> s >> t >> x;
        v.push_back({ s - x, x, 1 });
        v.push_back({ t - x, x, 0 });
    }
    sort(v.rbegin(), v.rend());
    multiset<int> sp;
    for (int i = 0; i < q; i++) {
        int d;
        cin >> d;
        while (!v.empty() && v.back().time <= d) {
            if (v.back().kind) sp.insert(v.back().corr);
            else sp.erase(sp.find(v.back().corr));
            v.pop_back();
        }
        cout << (sp.empty() ? -1 : *sp.begin()) << '\n';
    }
}