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;
#define FOR(i,a,b) for(int i=(a);i<(b);++i)
#define rep(i,n)   FOR(i,0,n)
#define pb emplace_back
typedef long long ll;
typedef pair<int,int> pint;

int n,q;
vector<tuple<int,int,int> > v;
int main(){
    int si,ti,xi,di;
    cin>>n>>q;
    rep(i,n){
        cin>>si>>ti>>xi;
        v.pb(si-xi,1,xi);
        v.pb(ti-xi,-1,xi);
    }
    v.pb(1000100010,0,0);
    sort(v.begin(),v.end());
    int cur=0;
    set<int> st;
    rep(i,q){
        cin>>di;
        while(get<0>(v[cur])<=di){
            if(get<1>(v[cur])==1){
                st.insert(get<2>(v[cur]));
            }
            else{
                st.erase(get<2>(v[cur]));
            }
            ++cur;
        }
        if(st.size()==0){
            cout<<-1<<endl;
        }
        else{
            cout<<*st.begin()<<endl;
        }
    }
    return 0;
}
