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 long long int lli;

int main() {
    int n, q, s, t, x, d;
    vector<pair<int, pair<int, int>>> events;

    cin >> n >> q;
    for (int i=0; i<n; i++) {
        cin >> s >> t >> x;
        events.push_back(make_pair(s-x, make_pair(1, x)));
        events.push_back(make_pair(t-x, make_pair(0, x)));
    }

    for (int i=0; i<q; i++) {
        cin >> d;
        events.push_back(make_pair(d, make_pair(2, 0)));
    }

    sort(events.begin(), events.end());

    multiset<int> st;
    for (auto& itr : events) {
        int a = itr.first, b = itr.second.first, c = itr.second.second;
        switch (b) {
        case 0:
            st.erase(c);
            break;
        case 1:
            st.insert(c);
            break;
        default:
            cout << ((st.empty()) ? -1 : *st.begin()) << endl;
            break;
        }
    }

    return 0;
}
