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;
#define rep(i, n) for (int i = 0; i < (n); i++)
#include <bits/stdc++.h>

const int MOD = 1000000007;

typedef pair<int, int> P;

int main() {
    int N, Q;
    cin >> N >> Q;
    vector<tuple<int, int, int>> a(N);
    rep(i, N) {
        int s, t, x;
        cin >> s >> t >> x;
        a[i] = make_tuple(x, s - x, t - x);
    }
    sort(a.begin(), a.end());

    set<P> s;
    rep(i, Q) {
        int q;
        cin >> q;
        s.insert({q, i});
    }

    vector<int> ans(Q, -1);
    rep(i, N) {
        int x, l, r;
        tie(x, l, r) = a[i];

        auto itr = s.lower_bound(P(l, -1));
        while (itr != s.end()) {
            if (itr->first >= r) break;
            ans[itr->second] = x;
            s.erase(itr++);
        }
    }

    rep(i, Q) {
        cout << ans[i] << endl;
    }
}
