# Pile of Crabs

Criterion 2021 Round 12
Limits 1s, 512 MB

There is a pile of crabs standing on one top of another.
There are total $N$ crabs numbered $1$ to $N$. The crab numbered $1$ is at the bottom of the pile. Crab numbered $2$ is on top of crab $1$ and so on. The crab numbered $N$ is at the top of the pile.
Each crab has an initial health value represented with an integer number.

You have to observe $Q$ events.
For each event, a crab numbered $X$ will start climbing from his position to the top of the pile. Every crab he will cross on his way, he will decrease their health value by $1$. If one’s health is equal to 0, the crab is dead and his value will not get decreased further. If the crab numbered $X$ is already on the top of the pile, he will not move.
If the crab numbered $X$ is already dead, he will not climb the pile. You have to report the crab is dead.

After observing all the events, you’ve to print the health value of each crab.

## Input

The first line on input consists of two integers $N$ and $Q$ $(3 ≤ N, Q ≤ 5 × 10^5)$ represents the number of crabs and the number of events respectively.
Each of the next $N$ lines consists of an integer value $H_i$ $(1 ≤ H_i ≤ 10^9)$ represents the health of $i^{th}$crab for each $i$ from $1$ to $N$.

Each of the next $Q$ lines consists of an integer $X$ represents the crab that will climb up the pile.

## Output

For each of the $Q$ events, if the crab numbered $X$ is already dead, print $Dead$ in separate lines. Otherwise, do not print anything.

After observing all the events, print a single line with $N$ integers $H_i$for each $i$ from $1$ to $N$seperated by space. $H_i$ represent the health of $i^{th}$ crab after all the events.

## Samples

InputOutput
4 3
2 3 1 4
2
3
1

Dead
2 2 0 2


After the first event, the health of crab 1, 2, 3, and 4 is equal to 2, 3, 0, 3 respectively.

In the second event, we can see crab 3 is already dead. So, it won’t move.

After the third event, the health of crabs 1, 2, 3, and 4 is equal to 2, 2, 0, 2 respectively.

InputOutput
10 16
19 5 26 71 16 2 22 8 85 24
8
1
2
1
4
4
9
9
9
5
8
2
6
10
6
9

Dead
13 0 24 65 10 0 18 1 78 17