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 <algorithm>
#include <tuple>
#include <set>

using namespace std;

#define rep(i,n) for(int i=0; i<(int)(n); i++)

int main() {
  int n, q, c = (int)1e9+7;
  cin >> n >> q;
  tuple<int, int> a[2*n+q];
  rep(i,n) {
    int s, t, x;
    cin >> s >> t >> x;
    a[2*i]   = tuple<int, int> (s - x, x);
    a[2*i+1] = tuple<int, int> (t - x, x);
  }
  rep(i,q) {
    int d;
    cin >> d;
    a[2*n+i] = tuple<int, int> (d, c);
  }
  
  sort(a, a+2*n+q);
  
  int r[q], j = 0;
  set<int> s = {c};
  rep(i,2*n+q) {
    int k = get<1>(a[i]);
    if(k == c) {
      r[j] = *s.begin();
      if(r[j] == c) r[j] = -1;
      j++;
    } else {
      if(s.count(k)) s.erase(k);
      else s.insert(k);
    }
  }
  
  rep(i,q) cout << r[i] << endl;
  return 0;
}