#include <bits/stdc++.h>
using namespace std;

int main(void){
  const int inf=1<<30;
  typedef tuple<int,int,int>t3;
  int n,Q,i,cur=0,s,t,x,v;
  priority_queue<t3,vector<t3>,greater<t3>>q;
  scanf("%d %d",&n,&Q);vector<int> ans(Q,-1),ds(Q);
  multiset<int>ms;ms.insert(inf);
  for (i=0;i<n;i++){
    scanf("%d %d %d",&s,&t,&x);
    q.push(make_tuple(s-x,x,1));
    q.push(make_tuple(t-x,x,0));
  }

  for (i=0;i<Q;i++)scanf("%d",&ds[i]);

  while (!q.empty()){
    t3 e=q.top();q.pop();
    tie(t,x,s)=e, v=*ms.begin();v=v!=inf?v:-1;
    while(cur<Q&&ds[cur]<t)ans[cur++]=v;
    if(s)ms.insert(x);
    else ms.erase(ms.find(x));
  }

  for (i=0;i<Q;i++)printf("%d\n",ans[i]);
  return 0;
}

### Prompt

In Cpp, your task is to solve the following problem:

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

### Response

```cpp
#include <bits/stdc++.h>
using namespace std;

int main(void){
  const int inf=1<<30;
  typedef tuple<int,int,int>t3;
  int n,Q,i,cur=0,s,t,x,v;
  priority_queue<t3,vector<t3>,greater<t3>>q;
  scanf("%d %d",&n,&Q);vector<int> ans(Q,-1),ds(Q);
  multiset<int>ms;ms.insert(inf);
  for (i=0;i<n;i++){
    scanf("%d %d %d",&s,&t,&x);
    q.push(make_tuple(s-x,x,1));
    q.push(make_tuple(t-x,x,0));
  }

  for (i=0;i<Q;i++)scanf("%d",&ds[i]);

  while (!q.empty()){
    t3 e=q.top();q.pop();
    tie(t,x,s)=e, v=*ms.begin();v=v!=inf?v:-1;
    while(cur<Q&&ds[cur]<t)ans[cur++]=v;
    if(s)ms.insert(x);
    else ms.erase(ms.find(x));
  }

  for (i=0;i<Q;i++)printf("%d\n",ans[i]);
  return 0;
}

```