Problem:
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Priority Queue

A priority queue is a data structure which maintains a set $S$ of elements, each of with an associated value (key), and supports the following operations:

$insert(S, k)$: insert an element $k$ into the set $S$

$extractMax(S)$: remove and return the element of $S$ with the largest key

Write a program which performs the $insert(S, k)$ and $extractMax(S)$ operations to a priority queue $S$.
The priority queue manages a set of integers, which are also keys for the priority.

Input

Multiple operations to the priority queue $S$ are given. Each operation is given by "insert $k$", "extract" or "end" in a line. Here, $k$ represents an integer element to be inserted to the priority queue.

The input ends with "end" operation.

Output

For each "extract" operation, print the element extracted from the priority queue $S$ in a line.

Constraints

The number of operations $\leq 2,000,000$

$0 \leq k \leq 2,000,000,000$

Sample Input 1

insert 8
insert 2
extract
insert 10
extract
insert 11
extract
extract
end

Sample Output 1

8
10
11
2

Solution in C (judge verdict: Time Limit Exceeded)

#include <stdio.h>
#include <string.h>
#include <stdlib.h>
#include <limits.h>

void Merge(long *A, long left, long mid, long right) {
  long n1,n2,*L,*R,i,j,k;
  n1 = mid -left;
  n2 = right - mid;
  L = (long*)malloc(sizeof(long) * (n1+1));
  R = (long*)malloc(sizeof(long) * (n2+1));
  for (i = 0; i< n1; i++) {
    L[i] = A[left+i];
  }
  for (i = 0; i < n2; i++) {
    R[i] = A[mid+i];
  }
  L[n1] = LONG_MAX; R[n2] = LONG_MAX;
  i = 0;j = 0;
  for(k = left; k < right; k++) {
    if (L[i] < R[j]) {
      A[k] = L[i];
      i++;
    }else {
      A[k] = R[j];
      j++;
    }
  }
  free(L);
  free(R);
}

void Merge_Sort(long *A, long left, long right) {
  if(left+1 < right) {
    long mid = (left + right)/2;
    Merge_Sort(A,left,mid);
    Merge_Sort(A,mid,right);
    Merge(A,left,mid,right);
  }
}


int main()
{
  long i,*S;
  char command[8];
  S = (long*)malloc(sizeof(long) * 2000000);
  i = 0;
  while(1) {
    scanf("%s",command);
    if(strcmp(command,"insert") == 0) {
      scanf("%ld",S+i);
      i++;
    }
    if(strcmp(command,"extract") == 0) {
      Merge_Sort(S,0,i);
      i--;
      printf("%ld\n",S[i]);
    }
    if(strcmp(command,"end") == 0) break;
  }
  return 0;
}