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;
typedef long long ll;
typedef pair<ll,ll> P;
typedef pair<P,int> event;
#define a first
#define b second
#define sz(x) (ll)((x).size())
#define pb push_back
#define mp make_pair 
#define bg begin()
#define ed end()
#define all(x) (x).bg,(x).ed
#define rep(i,n) for(ll i=0;i<n;i++)
#define rep1(i,n) for(ll i=1;i<=n;i++)

int main(){
	ll N,Q; cin>>N>>Q;
	set<event> se;
	multiset<ll> ans;
	rep(i,N){
		ll S,T,X; cin>>S>>T>>X;
		se.insert(mp(mp(S-X,X),1));
		se.insert(mp(mp(T-X,X),-1));
	}
	vector<ll> d(Q);
	rep(i,Q) cin>>d[i];

	ll i=0;
	auto itr=se.bg;
	while(i<Q){
		while(itr!=se.ed && (*itr).a.a<=d[i]){
			if((*itr).b==1) ans.insert((*itr).a.b);
			else{
				auto it=ans.find((*itr).a.b);
				ans.erase(it);
			}
			itr++;
		}
		if(ans.empty()) cout<<-1<<endl;
		else cout<<*ans.bg<<endl;
		i++;
	}
}