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<stdio.h>
#include<algorithm>
#include<set>
using namespace std;
#define fo(i,a,b) for(int i=a;i<=b;i++)
#define fd(i,a,b) for(int i=a;i>=b;i--)
int n,q,ss,tt,xx,et,dd,now;
set<int> s;
struct nod{
	int t,x;
	bool operator <(const nod &a)const{
		if (t==a.t) return x<a.x;
		return t<a.t;
	}
}e[510000];
int main(){
	scanf("%d%d",&n,&q);
	fo(i,1,n){
		scanf("%d%d%d",&ss,&tt,&xx);
		e[++et].t=ss-xx;
		e[et].x=xx;
		e[++et].t=tt-xx;
		e[et].x=-xx;
	}
	sort(e+1,e+et+1);
	now=1;
	while (q--){
		scanf("%d",&dd);
		while (now<=et&&e[now].t<=dd){
			if (e[now].x<0){
				s.erase(-e[now].x);
			}else{
				s.insert(e[now].x);
			}
			now++;
		}
		if (s.empty()) printf("-1\n");else printf("%d\n",*(s.begin()));
	}
	return 0;
}