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<int,int> P;
typedef pair<int,P> E;
#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(){
  int n,q;cin>>n>>q;
  vector<E> v;
  rep(i,n){
    int a,b,c;cin>>a>>b>>c;
    v.push_back(E(a-c,P(-1,c)));
    v.push_back(E(b-c,P(0,c)));
  }
  rep(i,q){
    int c;cin>>c;
    v.push_back(E(c,P(1,i)));
  }
  sort(all(v));
  multiset<int> m;
  for(auto a:v){
    int x=a.first,y=a.second.first,z=a.second.second;
    if(y==-1)m.insert(z);
    else if(y==0)m.erase(m.lower_bound(z));
    else cout<<(m.empty()?-1:*m.begin())<<endl;
  }
}