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 unsigned long long ull;
typedef long long ll;

int main(){
	int n, q;
	cin >> n >> q;

	vector<tuple<ll, ll, ll>> event;
	for(int i=0; i<n; i++){
		ll s, t, x;
		cin >> s >> t >> x;
		event.push_back(make_tuple(s-x, 0, x));
		event.push_back(make_tuple(t-x, -1, x));
	}
	for(int i=0; i<q; i++){
		ll d;
		cin >> d;
		event.push_back(make_tuple(d, 1, i));
	}
	sort(event.begin(), event.end());

	ll ans[q];
	multiset<ll> s;
	for(int i=0; i<event.size(); i++){
		ll x=get<0>(event[i]), y=get<1>(event[i]), z=get<2>(event[i]);
		if(y==0) s.insert(z);
		else if(y==-1) s.erase(z);
		else{
			if(s.empty()) ans[z]=-1;
			else ans[z]=*s.begin();
		}
	}
	for(int i=0; i<q; i++) cout << ans[i] << endl;
	return 0;
}