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>
#define rep(i,n) for(int i=0; i<n; i++)
#define PI 3.14159265359
#define INF 1000100100
#define MOD 1000000007
#define all(x) (x).begin(),(x).end()
typedef long long ll;
#define P pair<int, int>
#define PP pair<P,int>
#define T tuple<int,int,int> 
using namespace std;

int main(){
    int n,q; cin >> n >> q;
    vector<T> rw(n);
    rep(i,n){
        int a,b,c; cin >> a >> b >> c;
        rw[i]=T(c,a,b);
    }
    vector<int> d(q);
    rep(i,q) cin >> d[i];
    sort(all(rw));

    vector<int> ans(q,-1);

    set<P> s;
    rep(i,q) s.insert(P(d[i],i));

    rep(i,n){
        int x,l,r;
        tie(x,l,r) = rw[i];
        l-=x;
        r=r-x;
        auto it = s.lower_bound(P(l,-1));
        while(it!=s.end()){
            if(it->first >= r) break;
            ans[it->second]=x;
            s.erase(it++);
        }
    }

    rep(i,q) cout << ans[i] << endl;
    return 0;
}
