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<int,int> pii;
const int maxN = 1e3+7;
const int maxV = 90010;
//const int INF = 1e9+9;
//const ll INF = (1ll)<<60;
const int INF = 2e9+9;
const int MOD = 1e9+7;

map<int, vector<int> > S, T;
int d;
int n,q;
int main()
{
	scanf("%d%d",&n,&q);
	for(int i=1;i<=n;i++)
	{
		int s,t,x;
		scanf("%d%d%d",&s,&t,&x);
		S[s-x].push_back(x);
		T[t-x].push_back(x);
	}
	
	auto Sit = S.begin();
	auto Tit = T.begin();
	multiset<int> H;
	for (int i=1;i<=q;++i)
	{
		int d;
		scanf("%d",&d);
		while (Sit != S.end() && Sit->first <= d)
		{
			for (auto x : Sit->second)
				H.insert(x);
			Sit ++;
		}
		while (Tit != T.end() && Tit->first <= d)
		{
			for (auto x : Tit->second)
				H.erase(H.lower_bound(x));
			Tit ++;
		}
		int ans = 0;
		if(H.empty())
		{
			ans = -1;
		}
		else
			ans = *H.begin();
		cout<<ans<<endl;
	}

	return 0;
}