02. Icarus

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Problem 2. Icarus

Icarus is the majestic phoenix who has been alive from the beginning of creation. Icarus travels through different planes. When Icarus travels through a plane, he damages Reality itself with his overwhelming, beyond godlike flames.

You will receive a sequence of integers – the plane. After that you will receive 1 integer – an index in that sequence, which is Icarus’s starting position. Icarus’s INITIAL DAMAGE is 1.

You will then begin receiving commands in the following format: “{direction} {steps}”. The direction will be either “left” or “right”, and the steps will be an integer. Depending on the direction, Icarus must step through the sequence of integers to the left or right. Each time he steps on a NEW position, he damages it. In other words, he SUBTRACTS his current damage from the integer at that position. Walking left and right has its conditions though:

If Icarus passes beyond the start of the sequence (index: -1) while going left, he must go at the end of the sequence (index: length – 1).
If Icarus passes beyond the end of the sequence (index: length - 1) while going right, he must go at the start of the sequence (index: 0).

If 1 of the 2 cases stated above happens, Icarus increments his damage by 1.

The input ends when you receive the command “Supernova”. When that happens you must print what is left of the sequence.

Input

On the first input line you will get the sequence of integers, separated by spaces.
On the second input line you will get Icarus’s starting position.
On the next several input lines you will get the commands.

Output

As output you must print a single line containing the remaining elements of the sequence, separated by spaces.

Constrains

The integers in the sequence will be in range [0, 1000].
The initial position of Icarus will always be valid and inside the sequence’s indexes.
The direction will always be either “left” or “right”.
The steps will be in range [0, 1000].
There will be NO invalid input lines.
Allowed working time / memory: 100ms / 16MB.

Examples

Input

Output

Comments

50 50 25 50 50

left 2

right 2

left 2

right 2

Supernova

50 48 21 48 50

Initial index: 3

Initial state:

50 50 25 50 50

Go left 2 steps:

50 50 24 50 50

50 49 24 50 50

Go right 2 steps:

50 49 23 50 50

50 49 23 49 50

Go left 2 steps:

50 49 22 49 50

50 48 22 49 50

Go right 2 steps:

50 48 21 49 50

50 48 21 48 50

Final state:

50 48 21 48 50

5 3 5 5 5

left 5

Supernova

2 0 0 0 0

Initial index: 2

Initial state:

5 3 5 5 5

Go left 5 steps:

5 2 5 5 5

4 2 5 5 5

4 2 5 5 3

4 2 5 3 3

4 2 3 3 3

Go left 5 steps:

4 0 3 3 3

2 0 3 3 3

2 0 3 3 0

2 0 3 0 0

2 0 0 0 0

Final state:

2 0 0 0 0