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 ll = long long;


int main()
{
    int n, q; cin >> n >> q;
    vector<tuple<ll,ll,ll>> e;

    for(int i = 0; i < n; i++) {
        int s, t, x; cin >> s >> t >> x; 
        s -= x, t -= x;
        e.emplace_back(s, -1, x);
        e.emplace_back(t, 0, x);
    }

    for(int i = 0; i < q; i++) {
        int d; cin >> d;
        e.emplace_back(d, 1, i);
    }
    sort(e.begin(), e.end());

    //イベントソート(時系列順に見ていっていろいろする?)
    vector<ll> res(q);
    multiset<ll> se; //座標が入ってる
    for(auto p : e) {
        ll a, type, c; tie(a, type, c) = p;
        //工事が始まった
        if(type == -1) {
            se.insert(c);
        }
        //工事が終わった
        if(type == 0) {
            se.erase(se.lower_bound(c));
        }

        //
        if(type == 1) {
            res[c] = (se.size() ? *se.begin() : -1);
        }
    }
    for(auto i : res)cout << i << endl;

}