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;
struct node
{
  int d,co,flag;
  node (int d, int co, int flag) : d(d) , co(co),flag(flag) {}
  friend bool operator < (const node a,const node b)
  {
    return a.d < b.d;
  }
};
multiset<int>M;
vector<node>V;
int main()
{
  int n,m;
  scanf("%d%d",&n,&m);
  for(int i = 0 ; i < n ; i++)
  {
    int s,e,co;
    scanf("%d%d%d",&s,&e,&co);
    V.push_back(node(s-co,co,0));
    V.push_back(node(e-co,co,1));
  }
  sort(V.begin(),V.end());
  int k = 0;
  while(m--)
  {
    int q;
    scanf("%d",&q);
    while(k < V.size())
    {
      if(V[k].d <= q)
      {
        if(V[k].flag) M.erase(M.find(V[k].co));
        else M.insert(V[k].co); 
        k++;
      }
      else break;
     
    }
    int ans = - 1;
    if(M.size()) ans = *M.begin();
    cout<<ans<<endl;
  }
}