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>
#define rep(i,n) for(int i = 0; i < n; i++)
using namespace std;
typedef long long ll;
typedef pair<int,int> P;
const int MAX_Q = 200005;
ll D[MAX_Q];
vector<tuple<ll,ll,ll> > event;
multiset<ll> X;

int main()
{
	int N,Q;
	cin >> N >> Q;
	rep(i,N)
	{
		ll s,t,x;
		cin >> s >> t >> x;
		event.push_back(make_tuple(s-x,1,x));
		event.push_back(make_tuple(t-x,-1,x));
	}
	sort(event.begin(), event.end());
	rep(i,Q)
	{
		cin >> D[i];
	}
	int idx = 0;
	rep(i,Q)
	{
		//cout << get<0>(event[idx]) << " " << get<1>(event[idx]) << " " << get<2>(event[idx]) << endl;
		while (idx < event.size() && get<0>(event[idx]) <= D[i])
		{
			if (get<1>(event[idx]) == 1)
			{
				X.insert(get<2>(event[idx]));
			}
			else
			{
				X.erase(X.find(get<2>(event[idx])));
			}
			idx++;
		}

		if (X.empty())
		{
			cout << "-1" << endl;
		}
		else
		{
			cout << *X.begin() << endl;
		}
	}
	return 0;
}