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 ll long long
typedef pair<ll,ll> P;
typedef pair<ll,P> T;
#define M 1000000007
#define all(a) (a).begin(),(a).end()
#define rep(i,n) reps(i,0,n)
#define reps(i,m,n) for(int i=(m);i<(n);i++)
int main(){
  ll n,q;cin>>n>>q;
  vector<T> v;
  rep(i,n){
    ll s,t,x;cin>>s>>t>>x;
    v.push_back(T(s-x,P(-1,x)));
    v.push_back(T(t-x,P(0,x)));
  }
  rep(i,q){
    ll d;cin>>d;
    v.push_back(T(d,P(1,d)));
  }
  sort(all(v));
  multiset<ll> m;
  rep(i,v.size()){
    if(v[i].second.first==-1){
      m.insert(v[i].second.second);
    }else if(v[i].second.first==1){
      if(m.empty()) cout<<-1<<endl;
      else cout<<*m.begin()<<endl;
    }else{
      m.erase(m.lower_bound(v[i].second.second));
    }
  }
}