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;
#define rep(i, n) for(int i = 0, i##_len = (n); i < i##_len; ++i)
#define all(n) begin(n), end(n)

int main() {
  int n, q;
  cin >> n >> q;
  vector<tuple<int, int, int>> t;
  rep(i, n) {
    int l, r, x;
    cin >> l >> r >> x;
    l -= x;
    r -= x;
    t.push_back(make_tuple(l, 1, x));
    t.push_back(make_tuple(r, 0, x));
  }
  rep(i, q) {
    int d;
    cin >> d;
    t.push_back(make_tuple(d, 2, 0));
  }
  sort(all(t));
  set<int> st;
  for(auto v : t) {
    int l, b, x;
    tie(l, b, x) = v;
    if(b == 2)
      cout << (st.empty() ? -1 : *st.begin()) << endl;
    else if(b == 1)
      st.insert(x);
    else
      st.erase(x);
  }
}
