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 int long long
#define rep(i,n) for(int i=0;i<(n);i++)
#define repr(i,n) for(int i=(n)-1;i>=0;i++)
#define repf(i,j,n) for(int i=(j);i<(n);i++)

struct rw{
	int t,x,e;
	rw(){};
	rw(int t_,int x_,int e_){
		t=t_,x=x_,e=e_;
	};
	bool operator<(const rw& o)const {return t<o.t;}
};

signed main(){
	int n,q;cin>>n>>q;
	vector<int> d(q),ans;
	vector<rw> r;
	rep(i,n){
		int s,t,x;cin>>s>>t>>x;
		r.push_back(rw(s-x,x,1));
		r.push_back(rw(t-x,x,-1));} 
	for(auto&& u:d)cin>>u;
	sort(begin(r),end(r));

		int idx=0;
		multiset<int>s; 
	for(auto&& u:d){
		while(idx<r.size()&&r[idx].t<=u){
			if(r[idx].e==1)s.insert(r[idx].x);
			else s.erase(s.find(r[idx].x));
			idx++;
		}
		if(s.empty())ans.push_back(-1);
		else ans.push_back(*begin(s));
	}	
	for(auto&& u:ans)cout<<u<<endl;
}
