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;

int main(){
    int n,q;
    cin >> n >> q;
    vector<tuple<int,int,int>> vec;
    for(int i=0;i<n;i++){
        int s,t,x;
        cin >> s >> t >> x;
        vec.emplace_back(make_tuple(s-x,x,1));
        vec.emplace_back(make_tuple(t-x,x,0));
    }
    for(int i=0;i<q;i++){
        int d;
        cin >> d;
        vec.emplace_back(make_tuple(d,2e9,-1));
    }
    sort(vec.begin(),vec.end());
    set<int> st;
    st.insert(2e9);
    for(auto t:vec){

        if(get<2>(t) == 1){
            st.insert(get<1>(t));
        }
        else if(get<2>(t) == 0){
            st.erase(get<1>(t));
        }
        else if(get<2>(t) == -1){
            if(*st.begin()<2e9) cout << *st.begin() << endl;
            else cout << -1 << endl;
        }
    }
}