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
#if 1

#include <bits/stdc++.h>
using namespace std;
int n,q;
vector <pair <int,pair <int,int> > > a;
multiset <int> s;

int main()
{
    scanf("%d %d", &n, &q);
    int t,ss,x;
    for(int i = 1;i <= n;i++)
    {
        scanf("%d %d %d", &ss, &t, &x);
        a.push_back({ss-x,{1,x}});
        a.push_back({t-x,{-1,x}});
    }
    int i = 0;
    sort(a.begin(),a.end());
    while(q--)
    {
        int d;
        scanf("%d",&d);
        while(a[i].first <= d&&i < a.size())
        {
            if(a[i].second.first == 1)
            {
                s.insert(a[i].second.second);
            }
            else
            {
                s.erase(a[i].second.second);
            }
            i++;
        }
        if(s.size() > 0) printf("%d\n",*s.begin());
        else printf("-1\n");
    }
}

#endif // 1++
