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>
typedef long long ll; 
using namespace std;
const int maxn=2e5+10;
struct node{
	int val,pos,id;
	bool operator<(const node& a)const{
		return val<a.val;
	}
};
multiset<int>st;
node event[maxn<<1];
int main()
{
	int n,q;
	int num=0;
	scanf("%d%d",&n,&q);
	for(int i=1;i<=n;i++){
		int s,t,x;
		scanf("%d%d%d",&s,&t,&x);
		s-=x,t-=x;
		event[num++]={s,x,1};
		event[num++]={t,x,0};
	}
	sort(event,event+num);
	int now=0;
	for(int i=1;i<=q;i++){
		int d;
		scanf("%d",&d);
		while(now<num&&event[now].val<=d){
			if(event[now].id)st.insert(event[now].pos);
			else st.erase(st.find(event[now].pos));
			now++;
		}
		int ans=-1;
		if(st.size())ans=*st.begin();
		printf("%d\n",ans);
	}
}

