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 <cstdio>
#include <iostream>
#include <set>
#include <algorithm>
#define MN 401000

std::set<int> st;

struct xxx{
	int t, o, w;
	xxx(){}
	xxx(int a, int b, int c) {t = a; o = b; w = c;}
}b[MN];

bool cmp(xxx a, xxx b) {return a.t == b.t ? a.o < b.o : a.t < b.t;}

int main()
{
	int n, q; scanf("%d%d", &n, &q);
	int m = 0;
	for(int i = 1; i <= n; i++)
	{
		int s, t, c; scanf("%d%d%d", &s, &t, &c);
		s -= c; t -= c;
		b[++m] = xxx(s, 1, c);
		b[++m] = xxx(t, 0, c);
	}
	std::sort(b + 1, b + m + 1, cmp);
	int j = 1;
	for(int i = 1; i <= q; i++)
	{
		int d; scanf("%d", &d);
		while(j <= m && d >= b[j].t)
		{
			if(!b[j].o) st.erase(b[j].w);
			else st.insert(b[j].w);
			j++;
		}
		if(st.size() == 0) puts("-1");
		else printf("%d\n", *st.begin());
	}
	return 0;
}