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 lint = long long int;

int main() {
    lint n, q;
    cin >> n >> q;

    vector<tuple<lint, lint, lint>> query; // (time, type, info)
    for(lint i=0; i<n; i++) {
        lint s, t, x;
        cin >> s >> t >> x;
        query.emplace_back(s-x, 1, x);
        query.emplace_back(t-x, -1, x);
    }

    for(lint i=0; i<q; i++) {
        lint d;
        cin >> d;
        query.emplace_back(d, 2, -1); // info: dummy
    }

    sort(begin(query), end(query));

    multiset<lint> ms;
    for(auto e : query) {
        lint time, type, info;
        tie(time, type, info) = e;
        if(type == -1)  ms.erase(ms.find(info));
        if(type == 1)  ms.insert(info);
        if(type == 2) cout << (ms.empty() ? -1 : *ms.begin()) << endl;
    }
}