# Meteors

### Memory limit: 64 MB

Byteotian Interstellar Union (BIU) has recently discovered a new planet in
a nearby galaxy. The planet is unsuitable for colonisation due to strange
meteor showers, which on the other hand make it an exceptionally interesting
object of study.

The member states of BIU have already placed space stations close to the
planet's orbit. The stations' goal is to take samples of the rocks flying by.
The BIU Commission has partitioned the orbit into *M* sectors, numbered
from 1 to *M* where the sectors 1 and *M* are adjacent. In each sector
there is a single space station, belonging to one of the *N* member states.

Each state has declared a number of meteor samples it intends to gather before
the mission ends. Your task is to determine, for each state, when it can
stop taking samples, based on the meter shower predictions for the years to
come.

## Input

The first line of the standard input gives two integers, *N* and *M*, 1 ≤ N, M ≤ 300 000, separated by a single space, that denote,
respectively, the number of BIU member states and the number of sectors
the orbit has been partitioned into.

In the second line there are *M* integers *O*_{i}, 1 ≤ *O*_{i} ≤ N,
separated by single spaces, that denote the states owning stations in
successive sectors.

In the third line there are *N* integers *P*_{i}, 1 ≤ *P*_{i} ≤ 10^9,
separated by single spaces, that denote the numbers of meteor samples that
the successive states intend to gather.

In the fourth line there is a single integer *K*, 1 ≤ K ≤ 300 000,
that denotes the number of meteor showers predictions.
The following *K* lines specify the (predicted) meteor showers
chronologically. The i-th of these lines holds three integers
li, ri, ai (separated by single spaces), which denote that
a meteor shower is expected in sectors
li...ri if li ≤ ri or ri...li otherwise,
which should provide each station in those sectors with ai meteor samples.

In tests worth at least 20% of the points it additionally holds that
n, m, k ≤ 1000.

## Output

Your program should print *N* lines on the standard output.
The i-th of them should contain a single integer wi, denoting the number
of shower after which the stations belonging to the i-th state are
expected to gather at least ai samples, or the word *NIE* (Polish
for *no*) if that state is not expected to gather enough samples in the
foreseeable future.

## Example

For the input data:

3 5
1 3 2 1 3
10 5 7
3
4 2 4
1 3 1
3 5 2

the correct result is:

3
NIE
1

*Task authors: Paweł Mechlinski and Jakub Pachocki.*