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 in C (GCC 5.4.1) (judge verdict: Accepted)

#include<stdio.h>
#include<stdlib.h>
#include<stdint.h>
#include<inttypes.h>

typedef struct binaryHeap{
  void *array;
  size_t heap_size;
  size_t max_size;
  size_t val_size;
  int (*cmp) (const void *, const void *);
} heap;

heap* new_binary_heap (const size_t val_size, int (*cmpF) (const void *, const void *)) {
  heap *h = (heap *) calloc (1, sizeof (heap));
  h->array = malloc (val_size * (1 + 1));
  h->heap_size = 0;
  h->max_size = 1;
  h->val_size = val_size;
  h->cmp = cmpF;
  return h;
}

int32_t get_heap_size (const heap *h) {
  return h->heap_size;
}

int is_empty (const heap *h) {
  return h->heap_size == 0;
}

void free_heap (heap *h) {
  free (h->array);
  free (h);
}

void init_heap (heap *h) {
  h->heap_size = 0;
}

static inline void heap_func_swap (void * restrict a, void * restrict b, size_t val_size) {
  if ((val_size & 7) == 0) {
    uint64_t *p = (uint64_t *) a;
    uint64_t *q = (uint64_t *) b;
    val_size /= sizeof (uint64_t);
    while (val_size--) {
      const uint64_t tmp = *p;
      *p++ = *q;
      *q++ = tmp;
    }
  } else {
    uint8_t *p = (uint8_t *) a;
    uint8_t *q = (uint8_t *) b;
    while (val_size--) {
      const uint8_t tmp = *p;
      *p++ = *q;
      *q++ = tmp;
    }
  }
}

static inline void heap_func_copy (void * restrict dst, const void * restrict src, size_t val_size) {
  if ((val_size & 7) == 0) {
    const uint64_t *p = (const uint64_t *) src;
    uint64_t *q = (uint64_t *) dst;
    val_size /= sizeof (uint64_t);
    while (val_size--) {
      *q++ = *p++;
    }
  } else {
    const uint8_t *p = (const uint8_t *) src;
    uint8_t *q = (uint8_t *) dst;
    while (val_size--) {
      *q++ = *p++;
    }
  }
}

void push (heap * const h, const void *val) {
  if (h->heap_size == h->max_size) {
    h->max_size = 2 * h->max_size + 1;
    h->array = realloc (h->array, h->val_size * (h->max_size + 1));
  }
  h->heap_size++;
  uint8_t * const array = (uint8_t *) h->array;
  size_t k = h->heap_size;
  const size_t val_size = h->val_size;
  int (* const cmp) (const void *, const void *) = h->cmp;
  heap_func_copy(array + k * val_size, val, val_size);
  while (k > 1) {
    size_t parent = k / 2;
    if (cmp (array + parent * val_size, array + k * val_size) <= 0) {
      return;
    }
    heap_func_swap (array + parent * val_size, array + k * val_size, val_size);
    k = parent;
  }
}

void pop (heap * const h, void *res) {
  uint8_t * const array = (uint8_t *) h->array;
  const size_t val_size = h->val_size;
  if (res != NULL) {
    heap_func_copy (res, array + val_size, val_size);
  }
  heap_func_copy (array + val_size, array + val_size * h->heap_size, val_size);
  h->heap_size--;
  int (* const cmp) (const void *, const void *) = h->cmp;
  const size_t n = h->heap_size;
  size_t k = 1;
  while (2 * k  + 1 <= n) {
    const int c = cmp (array + val_size * 2 * k, array + val_size * (2 * k + 1));
    const size_t next = 2 * k + (c <= 0 ? 0 : 1);
    if (cmp (array + val_size * k, array + val_size * next) <= 0) return;
    heap_func_swap (array + val_size * k, array + val_size * next, val_size);
    k = next;
  }
  if (2 * k <= n && cmp (array + val_size * k, array + val_size * 2 * k) > 0) {
    heap_func_swap (array + val_size * k, array + val_size * 2 * k, val_size);
  }
}

void top (const heap *h, void *res) {
  uint8_t *array = (uint8_t *) h->array;
  const size_t val_size = h->val_size;
  if (res != NULL) {
    heap_func_copy (res, array + val_size, val_size);
  }
}

typedef int32_t i32;
typedef int64_t i64;

typedef struct node {
  i32 t;
  i32 x;
} node;

int cmp_node_time (const void *a, const void *b) {
  i32 d = ((node *)a)->t - ((node *)b)->t;
  return d == 0 ? 0 : d < 0 ? -1 : 1;
}

int cmp_int (const void *a, const void *b) {
  i32 d = *(i32 *)a - *(i32 *)b;
  return d == 0 ? 0 : d < 0 ? -1 : 1;
}

void run (void) {
  i32 n, q;
  scanf ("%" SCNi32 "%" SCNi32, &n, &q);
  node *s = (node *) calloc (n, sizeof (node));
  node *t = (node *) calloc (n, sizeof (node));
  for (i32 i = 0; i < n; ++i) {
    i32 a, b, x;
    scanf ("%" SCNi32 "%" SCNi32 "%" SCNi32, &a, &b, &x);
    s[i] = (node) {a - x, x};
    t[i] = (node) {b - x, x};
  }
  qsort (s, n, sizeof (node), cmp_node_time);
  qsort (t, n, sizeof (node), cmp_node_time);
  heap *now = new_binary_heap (sizeof (i32), cmp_int);
  heap *del = new_binary_heap (sizeof (i32), cmp_int);
  i32 i = 0, j = 0;
  while (q--) {
    i32 d;
    scanf ("%" SCNi32, &d);
    for(; i < n && s[i].t <= d; ++i) {
      push (now, &s[i].x);
    }
    for (; j < n && t[j].t <= d; ++j) {
      push (del, &t[j].x);
    }
    while (!is_empty (now) && !is_empty (del)) {
      i32 a, b;
      top (now, &a);
      top (del, &b);
      if (a != b) break;
      pop (now, NULL);
      pop (del, NULL);
    }
    if (is_empty (now)) {
      puts ("-1");
    } else {
      i32 v;
      top (now, &v);
      printf ("%" PRIi32 "\n", v);
    }
  }
}

int main (void) {
  run();
  return 0;
}