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 <vector>
#include <algorithm>
#include <queue>
#include <set>
#include <climits>
#include <math.h>
 
using namespace std;
typedef unsigned long ul;
typedef pair<int, int> P;

int main() {
	vector<P> events;
	int n,q,s,t,x,d;
	cin>>n>>q;
	for(int i=0;i<n;i++) {
		cin>>s>>t>>x;
		events.push_back(P(s-x,x));
		events.push_back(P(t-x,-x));
	}
	sort(events.begin(),events.end());

	set<int> block;
	for(int i=0,t=0;i<q;i++){
		cin>>d;
		for(;t<n*2&&events[t].first<=d;t++){
			x = events[t].second;
			if(x > 0) block.insert(x);
			else block.erase(-x);
		}
		if(block.empty()) cout<<-1<<endl;
		else cout<<*block.begin()<<endl;
	}
}