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;
const int N = 200001;
int main(){
	int n,q;
	cin>>n>>q;

	vector<pair<int,pair<int,int>>> pt;
	for(int i = 0; i < n; i++){
		int s,t,x;
		cin>>s>>t>>x;
		pt.push_back({x,{s-x,t-x}});
	}

	vector<int> res(N,-1);
	sort(pt.begin(),pt.end());

	set<int> st;
	map<int,int> mp;
	for(int i = 0; i < q; i++){
		int t;cin>>t;
		st.insert(t);
		mp[t] = i;
	}
	for(auto p : pt){
		int l = p.second.first;
		int r = p.second.second;
		int x = p.first;
		while(st.size()){
			auto it = st.lower_bound(l);
			if(it == st.end()) break;
			if(*it>=r) break;
			res[mp[*it]] = x;
			st.erase(it);
		}
	}

	for(int i = 0; i < q; i++) cout<<res[i]<<"\n";
}