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 <iostream>
#include <algorithm>
#include <vector>
#include <tuple>
#include <set>
#define pb push_back
using namespace std;
typedef tuple<int,int,int> T;
int a,b,c;
set<int> st;

int main(){
  int n,q;
  cin >> n >> q;
  int s[n],t[n],x[n],d[q];
  for(int i=0;i<n;i++) cin >> s[i] >> t[i] >> x[i];
  for(int i=0;i<q;i++) cin >> d[i];
  vector<T> event(0);
  for(int i=0;i<n;i++){
    event.pb(T(s[i]-x[i],1,x[i]));
    event.pb(T(t[i]-x[i],0,x[i]));
  }
  sort(event.begin(),event.end());
  int k=0;
  for(int i=0;i<2*n;i++){
    tie(a,b,c)=event[i];
    while(a>d[k]&&k<q){
      if(st.empty()) cout << -1 << endl;
      else cout << *st.begin() << endl;
      k++;
    }
    if(b) st.insert(c);
    else st.erase(c);
  }
  for(int i=k;i<q;i++) cout << -1 << endl;
}