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 REPR(i, n) for(int i = n; i >= 0; i--)
#define FOR(i, m, n) for(int i = m; i < n; i++)
#define ALL(v) v.begin(), v.end()
typedef long long ll;
using namespace std;

int main(){
  int n,q;
  cin >> n >> q;
  vector<tuple<int, int, int>> eve;
  REP(i,n){
    int s,t,x;
    cin >> s >> t >> x;
    eve.emplace_back(s-x, 1, x);
    eve.emplace_back(t-x, -1, x);
  }
  sort(ALL(eve));
  set<int> st;
  int t, id=0;
  REP(i,q){
    cin >> t;
    for(; id<eve.size() && get<0>(eve[id])<=t; id++){
      if(get<1>(eve[id])==1){
        st.insert(get<2>(eve[id]));
      }else{
        st.erase(get<2>(eve[id]));
      }
    }
    if(st.empty()) cout << -1 << '\n';
    else cout << *st.begin() << '\n';
  }
  return 0;
}
