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;
#define ll long long
#define pb push_back
#define ff first
#define ss second
#define mp make_pair
int main()
{
	int n,q;
	cin>>n>>q;
	vector<pair<ll,pair<ll,ll> > > p;
	for(ll i=0;i<n;i++)
	{
		ll s,t,x;
		cin>>s>>t>>x;
		p.pb(mp(x,mp(s-x,t-x-1)));
	}
	ll ans[q];
	multiset<pair<ll,ll> > s;
	for(ll i=0;i<q;i++)
	{
		ll d;
		cin>>d;
		s.insert(mp(d,i));
		ans[i]=-1;
	}
	sort(p.begin(),p.end());
	for(ll i=0;i<p.size();i++)
	{
		ll l=p[i].ss.ff;
		ll r=p[i].ss.ss;
		multiset<pair<ll,ll> >::iterator it;
		if(s.empty()) continue;
		it=s.lower_bound(mp(l,-1));
		while(s.size() && it!=s.end() && (*it).ff<=r)
		{
			ans[(*it).ss]=p[i].ff;
			s.erase(it++);
		}
	}
	for(ll i=0;i<q;i++)
	{
		cout<<ans[i]<<endl;
	}
	return 0;
}