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;
using P = pair<ll, ll>;
using E = tuple<ll, int, ll>;
const ll inf = numeric_limits<ll>::max()/3;
const ll mod = 1e9 + 7;

int main(void){
  int n,q;
  scanf("%d %d", &n, &q);
  vector< E > event;
  for(int i = 0;i < n;++i){
    ll s,t,x;
    scanf("%lld %lld %lld", &s, &t, &x);
    event.push_back(E{max(0LL,s - x),1,x});
    event.push_back(E{max(0LL,t - x),2,x});
  }
  for(int i = 0;i < q;++i){
    ll d;
    scanf("%lld", &d);
    event.push_back(E{d,3,-1});
  }
  sort(event.begin(),event.end());
  multiset< ll > res;
  for(E e : event) {
    ll t,x;
    int tag;
    tie(t,tag,x) = e;
    if(tag == 1){
      res.insert(x);
    }else if(tag == 2){
      auto ptr = res.find(x);
      res.erase(ptr);
    }else{
      if(res.empty()){
        puts("-1");
      }else{
        printf("%lld\n", *res.begin());
      }
    }
  }
  return 0;
}
