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<iostream>
#include<algorithm>
#include<vector>
#include<set>
#include<unordered_map>
using namespace std;
typedef long long ll;
#define N 200010
ll n,q;
unordered_map<ll,ll> mas;
struct ver{
  ll l,r,t;
  bool operator<(const ver&key)const{
      return this->t<key.t;
  }  
  ver(ll l,ll r,ll t){
      this->l=l,this->r=r,this->t=t;
  }
};
vector<ver> v;
ll ans[N];
int main(){
  cin>>n>>q;
  for(int i=0;i<n;i++){
      ll a,b,c;cin>>a>>b>>c;
      v.push_back(ver(a-c,b-c,c));
  }
  sort(v.begin(),v.end());
  set<ll> s;
  for(int i=0;i<q;i++){
      ll x;cin>>x;
      mas[x]=i;
      s.insert(x);
      ans[i]=-1;
  }
  for(auto p:v){
      ll l=p.l,r=p.r,t=p.t;
      while(s.size()>0){
	  auto it=s.lower_bound(l);
	  if(it==s.end())break;
	  if(*it>=r)break;
	  ans[mas[*it]]=t;
	  s.erase(it);
      }
  }
  for(int i=0;i<q;i++)cout<<ans[i]<<endl;
  return 0;
}
