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)<(n);(i)++)

int main(){


 int N,Q,i,j;
 typedef pair<int, int> P;
 cin >> N >> Q;

 vector<int> X(N),S(N),T(N),D(Q);
 set<pair<int, int>> shugo;

 rep(i,N){
  cin >> S[i] >> T[i] >> X[i];
}
 rep(i,Q){
  cin >> D[i];
 }
 rep(i,Q){
  shugo.insert(P(D[i],i));
}


vector<tuple<int, int, int>> a(N);
rep(i,N){
a[i] = tie(X[i], S[i], T[i]);
}
sort(a.begin(), a.end());

vector<int> ans;
rep(i,Q){
ans.push_back(-1);
}
rep(i,N){
 int x,l,r;
 tie(x,l,r)=a[i];
 auto it = shugo.lower_bound(P(l-x,-1));
 while(it!=shugo.end()){
  if((it->first) >= r-x){ break; }
  ans[it->second] = x;
  shugo.erase(it++);
}
}

rep(i,Q){
 cout << ans[i] << endl;
}

}