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;
const int maxn=2e5+7;
ll ans[maxn],d[maxn];
struct ver{
	ll l,r,c;
	bool operator<(const ver&key) const
	{
		return this->c < key.c;
	}
	ver(ll x,ll y,ll z):l(x),r(y),c(z)
	{
		
	}
};
unordered_map<ll,ll> mp;
vector<ver> v;
int main()
{
	ll n,q;scanf("%lld%lld",&n,&q);
	for(ll i=0;i<n;i++)
	{
		ll a,b,c;scanf("%lld%lld%lld",&a,&b,&c);
		v.push_back(ver(max(a-c,0ll),b-c-1,c));
	}
	sort(v.begin(),v.end());
	set<ll> s;
	for(ll i=1;i<=q;i++)
	{
		ll x;
		scanf("%lld",&x);
		mp[x]=i;s.insert(x);ans[i]=-1;
	}
	for(auto u : v)
	{
		ll l=u.l,r=u.r,c=u.c;
		while(s.size()>0)
		{
			auto it=s.lower_bound(l);
			if(it==s.end()) break;
			if((*it)>r) break;
			ans[mp[(*it)]]=c;
			s.erase((*it));
		}
	}
	for(ll i=1;i<=q;i++) cout<<ans[i]<<endl;
}