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 <iostream>
#include <queue>
#include <set>

using namespace std;
using pii = pair<int, int>;

#define rep(i,n) for(int i=0;i<(n);++i)
#define all(f,c,...) (([&](decltype((c)) cccc) { return (f)(begin(cccc), end(cccc), ## __VA_ARGS__); })(c))

using Events = pair<int, pii>;

int main() {
  int N, Q; cin >> N >> Q;

  priority_queue<Events, vector<Events>, greater<Events>> q;
  rep(i, N) {
    int s,t,x;
    cin >> s >> t >> x;
    q.emplace(s-x, pii(1, x));
    q.emplace(t-x, pii(-1, x));
  }

  set<int> s;
  rep(i, Q) {
    int d; cin >> d;
    while (!q.empty() && q.top().first <= d) {
      Events e = q.top(); q.pop();
      if (e.second.first == 1)
        s.insert(e.second.second);
      else
        s.erase(e.second.second);
    }
    if (s.empty())
      cout << -1 << endl;
    else
      cout << *s.begin() << endl;
  }

  return 0;
}
