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 ll;
typedef pair<int,int> P;
#define rep(i,N) for(ll (i)=0;(i)<(N);(i)++)
const int mod = 1000000007;

int main() {
  int n, q;
  cin >> n >> q;
  vector<tuple<int, int, int>> a(n);
  rep(i, n) {
    int s, t, x;
    cin >> s >> t >> x;
    s -=x;
    t -= x;
    a[i] = tie(x, s, t);
  }
  sort(a.begin(), a.end());

  set<P> st;
  rep(i, q) {
    int d;
    cin >> d;
    st.insert(P(d, i));
  }
  vector<int> ans(q, -1);
  rep(i, n) {
    int s, t, x;
    tie(x, s, t) = a[i];
    auto it = st.lower_bound(P(s, -1));
    while(it != st.end()) {
      if(it->first >= t) break;
      ans[it->second] = x;
      st.erase(it++);
    }
  }
  rep(i, q) {
    cout << ans[i] << endl;
  }
  
}