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;
using type = pair<int, int>;
using event = pair<int, type>;

int main() {
    int N, Q;
    vector<event> data;
    vector<int> res;
    multiset<int> pos;
    
    cin >> N >> Q;
    res.resize(Q);
    for (int i = 0; i < N; i++) {
        int s, t, x;
        cin >> s >> t >> x;
        data.push_back({s-x, type(-1, x)});
        data.push_back({t-x, type(0, x)});
    }
    for (int i = 0; i < Q; i++) {
        int d;
        cin >> d;
        data.push_back({d, type(1, i)});
    }
    
    sort(data.begin(), data.end());
    
    for (auto d : data) {
        int c, x; tie(c, x) = d.second;
        if (c == 1) res[x] = (pos.empty() ? -1 : *(pos.begin()));
        else if (c == -1) pos.insert(x);
        else pos.erase(pos.lower_bound(x));
    }
    
    for (auto ans : res) cout << ans << endl;
    return 0;
}