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 ll long long
#define ld long double
#define mod 1000000007
#define fi first
#define se second
#define pb push_back
#define IOS ios_base::sync_with_stdio(false);cout.tie(NULL);cin.tie(NULL);

using namespace std;

map<int,vector<int>> mp;
multiset<int> s;

int main()
{
    IOS;
    int n,q;
    cin>>n>>q;
    for(int i=0;i<n;i++)
    {
        int s,t,x;
        cin>>s>>t>>x;
        s-=x;
        t-=x;
        mp[s].pb(x);
        mp[t].pb(-x);
    }
    auto it=mp.begin();
    for(int i=0;i<q;i++)
    {
        int d;
        cin>>d;
        while(it!=mp.end() && (*it).fi<=d)
        {
            for(auto i:(*it).se)
            {
                if(i>0) s.insert(i);
                else s.erase(s.find(-i));
            }
            ++it;
        }
        if(s.size()) cout<<*(s.begin())<<endl;
        else cout<<-1<<endl;
    }
    return 0;
}
