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 llint;
typedef tuple<llint, llint, llint> TP;

int main() {
  int n, q;
  cin >> n >> q;
  vector<TP> v;
  for (int i = 0; i < n; i++) {
    llint s, t, x;
    cin >> s >> t >> x;
    v.emplace_back(s - x, 0, x);
    v.emplace_back(t - x, 1, x);
  }

  for (int i = 0; i < q; i++) {
    llint d;
    cin >> d;
    v.emplace_back(d, 2, i);
  }
  sort(v.begin(), v.end());

  vector<llint> ans(q);
  multiset<llint> se;
  for (auto &w : v) {
    llint s, k, x;
    tie(s, k, x) = w;
    if (k == 0) {
      se.insert(x);
    } else if (k == 1) {
      se.erase(se.lower_bound(x));
    } else {
      ans[x] = (se.empty() ? -1 : *se.begin());
    }
  }

  for (auto &w : ans) {
    cout << w << endl;
  }

  return 0;
}