Algo lab/zooma 1

Zooma 1

This task is motivated by Zuma, a video game by PopCap Games.

In this version of the game, there is a sequence of n colored balls that moves toward an exit. You can shoot another m colored balls into the sequence. Balls do not disappear in this version.

Find out the final sequence of the balls.

The balls in the original sequence are numbered from 1 to n. The balls that you shoot are numbered from n+1 to n+m.

Game play example

Consider the case where n=5 and m=4.

The original sequence has balls with these colors:

    1     2     3     4     5
    G     B     G     Y     Y

You have 4 balls numbered as this:

    6     7     8     9
    R     G     B     G

If you shoot your first ball to the location after ball 3, the sequence becomes

    1     2     3     *6*     4     5
    G     B     G     *R*     Y     Y

If you shoot your second ball to the location after ball 1, the sequence becomes

    1     *7*     2     3     6     4     5
    G     *G*     B     G     R     Y     Y

If you shoot your third ball to the location after ball 6, the sequence becomes

    1     7     2     3     6     *8*     4     5
    G     G     B     G     R     *B*     Y     Y

If you shoot your forth ball to the location after ball 5, the sequence becomes

    1     7     2     3     6     8     4     5     *9*
    G     G     B     G     R     B     Y     Y     *G*

and this is the final sequence.

Note: In this version, the colors of the balls are not relevant because balls do not disappear.

Input

• First line: n and m (n <= 1,000,000; m <= 1,000,000)
  • Notes: in the grader n <= 100,000; m <= 100,000. Time limit 1 second (easy), 3 second (hard)
• Next n lines: for 1≤i≤n, line 1+i specifies one integer c[i] the color of ball i.
• Next m lines: for 1≤j≤m, line 1+n+j specifies two integers d[j] and p[j]. d[j] is the color of ball n+j (this is your j-th ball), and p[j] is the number of the ball right after which you shoot this ball into the sequence. Note that p[j] < n+j.

Output

Your program should print n+m integers which are the ball numbers in the final sequence.

Example

This is the same example with colors: G = 1, B = 2, Y = 3, R = 4.

Input

5 4
1
2
1
3
3
4 3
1 1
2 6
1 5

Output

1
7
2
3
6
8
4
5
9

Test data

Download at: http://theory.cpe.ku.ac.th/~jittat/courses/01204212/tasks/zooma1/

Expected output for n10-3.in:

1
2
14
18
20
3
11
13
4
5
17
6
7
8
15
12
19
9
10
16

Expected output for n50-3.in (first 10 lines):

1
61
2
97
52
3
81
4
71
67
5