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;
 
int main() {
  int N,Q;
  cin >> N >> Q;
  vector<tuple<int,int,int>> v;
  vector<int> d(Q);
  for (int i=0;i<N;i++){
    int S,T,X;
    cin >> S >> T >> X;
    S-=X;
    T-=X;
    v.push_back(make_tuple(S,1,X));
    v.push_back(make_tuple(T,0,X));
  }
  for (int i=0;i<Q;i++){
    cin >> d[i];
  }
  sort(v.begin(),v.end());
  multiset<int> s;
  int last=-1000000007;
  int t=0;
  for (int i=0;i<Q;i++){
    while (last<get<0>(v[t])&&get<0>(v[t])<=d[i]){
      if (get<1>(v[t])==1){
        s.insert(get<2>(v[t]));
      }
      else {
        s.erase(get<2>(v[t]));
      }
      t++;
    }
    if (!s.empty()){
      cout << *begin(s) << endl;
    }
    else {
      cout << -1 << endl;
    }
    last=d[i];
  }
}