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 ll;

int main() {
    int n, q; cin >> n >> q;
    vector<tuple<int, int, int>> a;
    for (int i = 0; i < n; i++) {
        int s, t, x; cin >> s >> t >> x;
        a.push_back(make_tuple(s - x, 1, x));
        a.push_back(make_tuple(t - x, -1, x));
    }
    sort(a.begin(), a.end());
    set<int> st;
    int t = 0;
    for (int i = 0; i < q; i++) {
        int d; cin >> d;
        while (t < a.size() && get<0>(a[t]) <= d) {
            if (get<1>(a[t]) == 1) {
                st.insert(get<2>(a[t]));
            }
            else {
                st.erase(get<2>(a[t]));
            }
            t++;
        }
        if (st.empty()) {
            cout << -1 << endl;
        }
        else {
            cout << (*st.begin()) << endl;
        }
    }
    return 0;
}