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;

const int INF = 1e9;

int main() {
    int n, q;
    cin>>n>>q;

    tuple<int, int, int> events[2*n];
    for (int i=0; i<n; i++) {
        int s, t, x;
        cin>>s>>t>>x;
        events[2*i] = make_tuple(s-x, 1, x);
        events[2*i+1] = make_tuple(t-x, -1, x);
    }
    sort(events, events+2*n);

    set<int> s;
    int idx_d = 0;
    for (int i=0; i<q; i++) {
      int d;
      cin>>d;
      if (idx_d == 2*n) {
        cout<<-1<<endl;
        continue;
      }
      while (get<0>(events[idx_d]) <= d) {
        if (get<1>(events[idx_d]) == 1) {
          s.insert(get<2>(events[idx_d]));
        } else {
          s.erase(get<2>(events[idx_d]));
        }
        ++idx_d;
        if (idx_d == 2*n) {
          break;
        }
      }
      if (s.size() == 0) {
        cout<<-1<<endl;
      } else {
        cout<<*s.begin()<<endl;
      }
    }
}