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;

using i64 = int64_t;

struct Event{
    int event, tm, x;
    bool operator<(const Event &rhs)const{
        if(tm == rhs.tm)return event < rhs.event;
        return tm < rhs.tm;
    }
};

int main(){
    int n, q;
    cin >> n >> q;
    vector<Event> v;
    for(int i=0;i<n;++i){
        int s, t, x;
        cin >> s >> t >> x;
        v.push_back({1, s-x, x});
        v.push_back({-1, t-x, x});
    }

    sort(v.begin(), v.end());
    set<int> st;
    int idx = 0;
    for(int i=0;i<q;++i){
        int d;
        cin >> d;
        while(idx < (int)v.size() && d >= v[idx].tm){
            if(v[idx].event == 1){
                st.insert(v[idx].x);
            }else{
                st.erase(v[idx].x);
            }
            idx++;
        }
        if(st.empty())cout << -1;
        else cout << *(st.begin());
        cout << endl;
    }

    return 0;
}