Problem:
 Score : 500 points    Problem Statement 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.        Sample Input 1 4 6
1 3 2
7 13 10
18 20 13
3 4 2
0
1
2
3
5
8      Sample Output 1 2
2
10
-1
13
-1  The first person starts coordinate 0 at time 0 and stops walking at coordinate 2 when reaching a point blocked by the first roadwork at time 2 .  The second person starts coordinate 0 at time 1 and reaches coordinate 2 at time 3 . The first roadwork has ended, but the fourth roadwork has begun, so this person also stops walking at coordinate 2 .  The fourth and sixth persons encounter no roadworks while walking, so they walk forever. The output for these cases is -1 .

Solution (Python):
from heapq import *

class MultisetBIT:
    """
    最大値が小さい数について、その重複を許した集合を管理する。
    最大値 maxvalue を受け取り、[0, maxvalue] を管理する。
    counter は辞書型かリスト型で、counter[i] が i の個数を持つことを仮定する。
    counter が与えられなかった場合は、全て個数 0 で初期化される。
    基本的に閉区間で管理する。
    内部では受け取った数を +1 したものをindexとして持っているので注意。
    """

    __slots__ = ["n", "k", "data"]

    def __init__(self, maxvalue, counter = None):
        self.n = maxvalue + 1
        self.k = 1 << ((self.n + 1).bit_length() - 1)
        self.data = [0] * (self.n + 1)
        if counter is not None:
            self.update(counter)
        
    def update(self, counter):
        """
        counter を受け取って、それを反映させる。
        counter は辞書型かリスト型で、counter[i] が i の個数を持つことを仮定する。
        計算量は、n を要素の最大値として、 O(n) となる。
        """
        if isinstance(counter, list):
            self.data = [0] + counter + [0] * (self.n - len(counter))
        else:
            self.data = [0] * (self.n + 1)
            for k, v in counter.items():
                self.data[k + 1] = v
        for i in range(1, self.n + 1):
            if i + (i & -i) <= self.n:
                self.data[i + (i & -i)] += self.data[i]

    def add(self, value):
        """
        与えられた引数を Multiset に加える。
        計算量は、n を要素の最大値として、 O(log n) となる。
        """
        value += 1
        while value <= self.n:
            self.data[value] += 1
            value += value & -value

    def pop(self, value):
        """
        Multiset から与えられた引数を取り除く。
        与えられた引数が Multiset に入っているかのチェックは行わなず、
        単にその個数を 1 減らすだけなので注意。
        計算量は、n を要素の最大値として、 O(log n) となる。
        """
        value += 1
        while value <= self.n:
            self.data[value] -= 1
            value += value & -value

    def count_le(self, value):
        """
        Multiset 内の要素 elem のうち、0 <= elem <= value を満たすものを数える。
        計算量は、n を要素の最大値として、 O(log n) となる。
        """
        value += 1
        ret = 0
        while value > 0:
            ret += self.data[value]
            value -= value & -value
        return ret

    def count(self, first, last):
        """
        Multiset 内の要素 elem のうち、first <= elem <= last を満たすものを数える。
        計算量は、n を要素の最大値として、 O(log n) となる。
        """
        last += 1
        ret = 0
        while first < last:
            ret += self.data[last]
            last -= last & -last
        while last < first:
            ret -= self.data[first]
            first -= first & -first
        return ret

    def bisect(self, count):
        """
        Multiset 内の要素 elem のうち、count <= count_le(elem) を満たす最小のelemを返す。
        計算量は、n を要素の最大値として、 O(log n) となる。
        """
        ret = 0
        k = self.k
        while k > 0:
            if ret + k <= self.n and self.data[ret + k] < count:
                count -= self.data[ret + k]
                ret += k
            k //= 2
        return ret

    def lower_bound(self, value):
        """
        Multiset 内の要素 elem のうち、value <= elem を満たす最小のelemを返す。
        計算量は、n を要素の最大値として、 O(log n) となる。
        """
        return self.bisect(self.count_le(value - 1) + 1)

    def upper_bound(self, value):
        """
        Multiset 内の要素 elem のうち、value < elem を満たす最小のelemを返す。
        計算量は、n を要素の最大値として、 O(log n) となる。
        """
        return self.bisect(self.count_le(value) + 1)


N, Q = map(int, input().split())
STXs = [tuple(map(int, input().split())) for _ in range(N)]
Ds = [int(input()) for _ in range(Q)]

i2X = sorted(map(lambda t: t[2], STXs))
X2i = {X:i for i, X in enumerate(i2X)}
max_i = len(i2X) - 1
mbit = MultisetBIT(max_i)

events = []
for S, T, X in STXs:
    events.append( ((S - X) << 32) + (X2i[X] << 1)     )
    events.append( ((T - X) << 32) + (X2i[X] << 1) + 1 )
heapify(events)

mask = (1 << 32) - 1
for D in Ds:
    while events:
        if events[0] % 2 == 0:
            if (events[0] >> 32) <= D:
                e = heappop(events)
                mbit.add((e & mask) >> 1)
            else:
                break
        else:
            if (events[0] >> 32) <= D:
                e = heappop(events)
                mbit.pop((e & mask) >> 1)
            else:
                break
    
    ans_i = mbit.lower_bound(0)
    print(-1 if ans_i > max_i else i2X[ans_i])

Solution (Python):
class AVLtree:
    """
    参考：http://www.nct9.ne.jp/m_hiroi/light/pyalgo12.html
    insert : 挿入
    erase : 削除
    lower_bound(x) : x <= v なる最小のv、なければ-float("inf")、最小値はlower(-float("inf"))
    upper_bound(x) : v < x なる最大のv、なければfloat("inf")、最大値はupper(float("inf"))
    print(avltree) : デバッグ用
    """
 
    def __init__(self):
        self.root = None

        
    def insert(self, x):
        if self.root is None:
            self.root = Node(x)
            return
        q = []
        node = self.root
        while True:
            if node.val == x:
                return
            elif x < node.val:
                q.append((node, 1))
                if node.left is None:
                    node.left = Node(x)
                    break
                node = node.left
            else:
                q.append((node, -1))
                if node.right is None:
                    node.right = Node(x)
                    break
                node = node.right
                
        
        new_node = None
        while q:
            node, key = q.pop()
            node.bal += key
            bal = node.bal
            if not bal:
                return
            if bal == 2:
                if node.left.bal == -1:
                    node.left = node.left._rotateL()
                    new_node = node._rotateR()
                    new_node._update_bal()
                else:
                    new_node = node._rotateR()
                    new_node.bal = 0
                    node.bal = 0
                break
            elif bal == -2:
                if node.right.bal == 1:
                    node.right = node.right._rotateR()
                    new_node = node._rotateL()
                    new_node._update_bal()
                else:
                    new_node = node._rotateL()
                    new_node.bal = 0
                    node.bal = 0
                break
        if q:
            node, key = q.pop()
            if key == 1:
                node.left = new_node
            else:
                node.right = new_node
        elif new_node is not None:
            self.root = new_node

            
    def erase(self, x):
        if self.root is None:
            return
        q = []
        node = self.root
        while node is not None:
            if node.val == x:
                break
            if x < node.val:
                q.append((node, 1))
                node = node.left
            else:
                q.append((node, -1))
                node = node.right
        else:
            return
        if node.left is not None and node.right is not None:
            q.append((node, -1))
            min_node = node.right
            while min_node.left is not None:
                q.append((min_node, 1))
                min_node = min_node.left
            node.val = min_node.val
            node = min_node
        if q:
            pre, key = q[-1]
        else:
            pre = None
        if node.left is None:
            cnode = node.right
        else:
            cnode = node.left
        if pre is None:
            self.root = cnode
            return
        if key == 1:
            pre.left = cnode
        else:
            pre.right = cnode
        
        
        while q:
            new_node = None
            node, key = q.pop()
            node.bal -= key
            bal = node.bal
            if bal == 2:
                if node.left.bal == -1:
                    node.left = node.left._rotateL()
                    new_node = node._rotateR()
                    new_node._update_bal()
                else:
                    new_node = node._rotateR()
                    if not new_node.bal:
                        new_node.bal = -1
                        node.bal = 1
                    else:
                        new_node.bal = 0
                        node.bal = 0
            elif bal == -2:
                if node.right.bal == 1:
                    node.right = node.right._rotateR()
                    new_node = node._rotateL()
                    new_node._update_bal()
                else:
                    new_node = node._rotateL()
                    if not new_node.bal:
                        new_node.bal = 1
                        node.bal = -1
                    else:
                        new_node.bal= 0
                        node.bal = 0
            elif bal:
                break
            if new_node is not None:
                if not q:
                    self.root = new_node
                    return
                node, key = q[-1]
                if key == 1:
                    node.left = new_node
                else:
                    node.right = new_node
                if new_node.bal:
                    break

                    
    def lower_bound(self, x):
        res = float("inf")
        node = self.root
        while node is not None:
            if x <= node.val:
                res = node.val
                node = node.left
            else:
                node = node.right
        return res
    
    
    def upper_bound(self, x):
        res = -float("inf")
        node = self.root
        while node is not None:
            if x <= node.val:
                node = node.left
            else:
                res = node.val
                node = node.right
        return res
    
    
    def __str__(self):
        if self.root is None:
            return "[]"
        buff = "["
        for x in self.root._dfs():
            buff += str(x)+", "
        buff = buff.rstrip(", ")
        buff += "]"
        return buff


class Node:
    def __init__(self, x):
        self.val = x
        self.left = None
        self.right = None
        self.bal = 0 
    
    
    def _rotateR(self):
        nodeL = self.left
        self.left = nodeL.right
        nodeL.right = self
        return nodeL
    
    
    def _rotateL(self):
        nodeR = self.right
        self.right = nodeR.left
        nodeR.left = self
        return nodeR
    
    
    def _update_bal(self):
        if self.bal == 1:
            self.right.bal = -1
            self.left.bal = 0
        elif self.bal == -1:
            self.right.bal = 0
            self.left.bal = 1
        else:
            self.right.bal = 0
            self.left.bal = 0
        self.bal = 0
    
    
    def _dfs(self):
        if self is not None:
            if self.left is not None:
                for x in self.left._dfs():
                    yield x
            yield self.val
            if self.right is not None:
                for x in self.right._dfs():
                    yield x

n,q = map(int, input().split())
e = []
for i in range(n):
  s,t,x = map(int, input().split())
  e.append((s-x,x,i))
  e.append((t-x,x,i))
e.sort(key=lambda x:x[0])
D = [int(input()) for _ in range(q)]
avl = AVLtree()
ans = []
f = [0]*n
j = 0
N = 2*n
for d in D:
  while j < N and e[j][0] <= d:
    _,x,i = e[j]
    if f[i]:
      avl.erase((x,i))
    else:
      avl.insert((x,i))
      f[i] = 1
    j += 1
  m = avl.lower_bound((-float("inf"),0))
  ans.append(m[0] if m != float("inf") else -1)

for i in ans:
  print(i)

Solution (Python):
class AVLtree:
    """
    参考：http://www.nct9.ne.jp/m_hiroi/light/pyalgo12.html
    insert : 挿入
    erase : 削除
    lower_bound(x) : x <= v なる最小のv、なければ-float("inf")、最小値はlower(-float("inf"))
    upper_bound(x) : v < x なる最大のv、なければfloat("inf")、最大値はupper(float("inf"))
    print(avltree) : デバッグ用
    """
 
    def __init__(self):
        self.root = None
        self.num = 0
        
    def insert(self, x):
        if self.root is None:
            self.root = Node(x)
            self.num += 1
            return
        q = []
        node = self.root
        while True:
            if node.val == x:
                return
            elif x < node.val:
                q.append((node, 1))
                if node.left is None:
                    node.left = Node(x)
                    break
                node = node.left
            else:
                q.append((node, -1))
                if node.right is None:
                    node.right = Node(x)
                    break
                node = node.right
        self.num += 1
        
        
        new_node = None
        while q:
            node, key = q.pop()
            node.bal += key
            node.size += 1
            bal = node.bal
            if not bal:
                while q:
                    node, key = q.pop()
                    node.size += 1
                return
            if bal == 2:
                if node.left.bal == -1:
                    node.left = node.left._rotateL()
                    new_node = node._rotateR()
                    new_node._update_bal()
                else:
                    new_node = node._rotateR()
                    new_node.bal = 0
                    node.bal = 0
                break
            elif bal == -2:
                if node.right.bal == 1:
                    node.right = node.right._rotateR()
                    new_node = node._rotateL()
                    new_node._update_bal()
                else:
                    new_node = node._rotateL()
                    new_node.bal = 0
                    node.bal = 0
                break
        if q:
            node, key = q.pop()
            node.size += 1
            if key == 1:
                node.left = new_node
            else:
                node.right = new_node
        elif new_node is not None:
            self.root = new_node
        while q:
            node, key = q.pop()
            node.size += 1

            
    def erase(self, x):
        if self.root is None:
            return
        q = []
        node = self.root
        while node is not None:
            if node.val == x:
                break
            if x < node.val:
                q.append((node, 1))
                node = node.left
            else:
                q.append((node, -1))
                node = node.right
        else:
            return

        self.num -= 1
        if node.left is not None and node.right is not None:
            q.append((node, -1))
            min_node = node.right
            while min_node.left is not None:
                q.append((min_node, 1))
                min_node = min_node.left
            node.val = min_node.val
            node = min_node
        if q:
            pre, key = q[-1]
        else:
            pre = None
        if node.left is None:
            cnode = node.right
        else:
            cnode = node.left
        if pre is None:
            self.root = cnode
            return
        if key == 1:
            pre.left = cnode
        else:
            pre.right = cnode
        
        
        while q:
            new_node = None
            node, key = q.pop()
            node.bal -= key
            node.size -= 1
            bal = node.bal
            if bal == 2:
                if node.left.bal == -1:
                    node.left = node.left._rotateL()
                    new_node = node._rotateR()
                    new_node._update_bal()
                else:
                    new_node = node._rotateR()
                    if not new_node.bal:
                        new_node.bal = -1
                        node.bal = 1
                    else:
                        new_node.bal = 0
                        node.bal = 0
            elif bal == -2:
                if node.right.bal == 1:
                    node.right = node.right._rotateR()
                    new_node = node._rotateL()
                    new_node._update_bal()
                else:
                    new_node = node._rotateL()
                    if not new_node.bal:
                        new_node.bal = 1
                        node.bal = -1
                    else:
                        new_node.bal= 0
                        node.bal = 0
            elif bal:
                break
            if new_node is not None:
                if not q:
                    self.root = new_node
                    return
                node, key = q[-1]
                if key == 1:
                    node.left = new_node
                else:
                    node.right = new_node
                if new_node.bal:
                    break
        while q:
            node, key = q.pop()
            node.size -= 1
                    
    def lower_bound(self, x):
        res = float("inf")
        node = self.root
        while node is not None:
            if x <= node.val:
                res = node.val
                node = node.left
            else:
                node = node.right
        return res
    
    
    def upper_bound(self, x):
        res = -float("inf")
        node = self.root
        while node is not None:
            if x <= node.val:
                node = node.left
            else:
                res = node.val
                node = node.right
        return res
    
    def __len__(self):
        return self.num

    def __getitem__(self, key):
        if key < 0:
            key += self.num
        key += 1
        node = self.root
        while True:
            idx = node.left.size + 1 if node.left is not None else 1
            if idx <= key:
                key -= idx
                if not key:
                    break
                node = node.right
            else:
                node = node.left
        return node.val

    
    def __str__(self):
        if self.root is None:
            return "[]"
        buff = "["
        for x in self.root._dfs():
            buff += str(x)+", "
        buff = buff.rstrip(", ")
        buff += "]"
        return buff


class Node:
    def __init__(self, x):
        self.val = x
        self.left = None
        self.right = None
        self.bal = 0 
        self.size = 1
    
    def _rotateR(self):
        nodeL = self.left
        nodeLL_size = nodeL.left.size if nodeL.left is not None else 0
        nodeR_size = self.right.size if self.right is not None else 0
        self.size -= nodeLL_size + 1
        nodeL.size += nodeR_size + 1
        self.left = nodeL.right
        nodeL.right = self
        return nodeL
    
    
    def _rotateL(self):
        nodeR = self.right
        nodeRR_size = nodeR.right.size if nodeR.right is not None else 0
        nodeL_size = self.left.size if self.left is not None else 0
        self.size -= nodeRR_size + 1
        nodeR.size += nodeL_size + 1
        self.right = nodeR.left
        nodeR.left = self
        return nodeR
    
    
    def _update_bal(self):
        if self.bal == 1:
            self.right.bal = -1
            self.left.bal = 0
        elif self.bal == -1:
            self.right.bal = 0
            self.left.bal = 1
        else:
            self.right.bal = 0
            self.left.bal = 0
        self.bal = 0
    
    
    def _dfs(self):
        if self is not None:
            if self.left is not None:
                for x in self.left._dfs():
                    yield x
            yield self.val
            if self.right is not None:
                for x in self.right._dfs():
                    yield x
                    

n,q = map(int, input().split())
e = []
for i in range(n):
  s,t,x = map(int, input().split())
  e.append((s-x,x,i))
  e.append((t-x,x,i))
e.sort(key=lambda x:x[0])
D = [int(input()) for _ in range(q)]
avl = AVLtree()
ans = []
f = [0]*n
j = 0
N = 2*n
for d in D:
  while j < N and e[j][0] <= d:
    _,x,i = e[j]
    if f[i]:
      avl.erase((x,i))
    else:
      avl.insert((x,i))
      f[i] = 1
    j += 1
  m = avl.lower_bound((-float("inf"),0))
  ans.append(m[0] if m != float("inf") else -1)

for i in ans:
  print(i)

Solution (Python):
class AVLtree:
    """
    参考：http://www.nct9.ne.jp/m_hiroi/light/pyalgo12.html
    insert : 挿入
    erase : 削除
    lower_bound(x) : x <= v なる最小のv、なければ-float("inf")、最小値はlower(-float("inf"))
    upper_bound(x) : v < x なる最大のv、なければfloat("inf")、最大値はupper(float("inf"))
    print(avltree) : デバッグ用
    """
 
    def __init__(self):
        self.root = None

        
    def insert(self, x):
        if self.root is None:
            self.root = Node(x)
            return
        q = []
        node = self.root
        while True:
            if node.val == x:
                return
            elif x < node.val:
                q.append((node, 1))
                if node.left is None:
                    node.left = Node(x)
                    break
                node = node.left
            else:
                q.append((node, -1))
                if node.right is None:
                    node.right = Node(x)
                    break
                node = node.right
                
        
        new_node = None
        while q:
            node, key = q.pop()
            node.bal += key
            bal = node.bal
            if not bal:
                return
            if bal == 2:
                if node.left.bal == -1:
                    node.left = node.left._rotateL()
                    new_node = node._rotateR()
                    new_node._update_bal()
                else:
                    new_node = node._rotateR()
                    new_node.bal = 0
                    node.bal = 0
                break
            elif bal == -2:
                if node.right.bal == 1:
                    node.right = node.right._rotateR()
                    new_node = node._rotateL()
                    new_node._update_bal()
                else:
                    new_node = node._rotateL()
                    new_node.bal = 0
                    node.bal = 0
                break
        if q:
            node, key = q.pop()
            if key == 1:
                node.left = new_node
            else:
                node.right = new_node
        elif new_node is not None:
            self.root = new_node

            
    def erase(self, x):
        if self.root is None:
            return
        q = []
        node = self.root
        while node is not None:
            if node.val == x:
                break
            if x < node.val:
                q.append((node, 1))
                node = node.left
            else:
                q.append((node, -1))
                node = node.right
        else:
            return
        if node.left is not None and node.right is not None:
            q.append((node, -1))
            min_node = node.right
            while min_node.left is not None:
                q.append((min_node, 1))
                min_node = min_node.left
            node.val = min_node.val
            node = min_node
        if q:
            pre, key = q[-1]
        else:
            pre = None
        if node.left is None:
            cnode = node.right
        else:
            cnode = node.left
        if pre is None:
            self.root = cnode
            return
        if key == 1:
            pre.left = cnode
        else:
            pre.right = cnode
        
        
        while q:
            new_node = None
            node, key = q.pop()
            node.bal -= key
            bal = node.bal
            if bal == 2:
                if node.left.bal == -1:
                    node.left = node.left._rotateL()
                    new_node = node._rotateR()
                    new_node._update_bal()
                else:
                    new_node = node._rotateR()
                    if not new_node.bal:
                        new_node.bal = -1
                        node.bal = 1
                    else:
                        new_node.bal = 0
                        node.bal = 0
            elif bal == -2:
                if node.right.bal == 1:
                    node.right = node.right._rotateR()
                    new_node = node._rotateL()
                    new_node._update_bal()
                else:
                    new_node = node._rotateL()
                    if not new_node.bal:
                        new_node.bal = 1
                        node.bal = -1
                    else:
                        new_node.bal= 0
                        node.bal = 0
            elif bal:
                break
            if new_node is not None:
                if not q:
                    self.root = new_node
                    return
                node, key = q[-1]
                if key == 1:
                    node.left = new_node
                else:
                    node.right = new_node
                if new_node.bal:
                    break

                    
    def lower_bound(self, x):
        res = float("inf")
        node = self.root
        while node is not None:
            if x <= node.val:
                res = node.val
                node = node.left
            else:
                node = node.right
        return res
    
    
    def upper_bound(self, x):
        res = -float("inf")
        node = self.root
        while node is not None:
            if x <= node.val:
                node = node.left
            else:
                res = node.val
                node = node.right
        return res
    
    
    def __str__(self):
        if self.root is None:
            return "[]"
        buff = "["
        for x in self.root._dfs():
            buff += str(x)+", "
        buff = buff.rstrip(", ")
        buff += "]"
        return buff


class Node:
    def __init__(self, x):
        self.val = x
        self.left = None
        self.right = None
        self.bal = 0 
    
    
    def _rotateR(self):
        nodeL = self.left
        self.left = nodeL.right
        nodeL.right = self
        return nodeL
    
    
    def _rotateL(self):
        nodeR = self.right
        self.right = nodeR.left
        nodeR.left = self
        return nodeR
    
    
    def _update_bal(self):
        if self.bal == 1:
            self.right.bal = -1
            self.left.bal = 0
        elif self.bal == -1:
            self.right.bal = 0
            self.left.bal = 1
        else:
            self.right.bal = 0
            self.left.bal = 0
        self.bal = 0
    
    
    def _dfs(self):
        if self is not None:
            if self.left is not None:
                for x in self.left._dfs():
                    yield x
            yield self.val
            if self.right is not None:
                for x in self.right._dfs():
                    yield x

n,q = map(int, input().split())
e = []
for i in range(n):
  s,t,x = map(int, input().split())
  e.append((s-x,x,i))
  e.append((t-x,x,i))
e.sort(key=lambda x:x[0])
D = [int(input()) for _ in range(q)]
avl = AVLtree()
ans = []
f = [0]*n
j = 0
N = 2*n
for d in D:
  while j < N and e[j][0] <= d:
    _,x,i = e[j]
    if f[i]:
      avl.erase((x,i))
    else:
      avl.insert((x,i))
      f[i] = 1
    j += 1
  m = avl.lower_bound((-float("inf"),0))
  ans.append(m[0] if m != float("inf") else -1)

for i in ans:
  print(i)