# Coin Distribution and Prime Seekers
## Problem Statement
There are $n$ people standing in a line, indexed from $1$ to $n$. Initially, each person has $0$ coins.
You are given $q$ queries. Each query is defined by three integers: $l, r, y$. For each query, every person with an index $i$ such that $l \le i \le r$ receives $y$ additional coins.
After all $q$ queries have been processed, you need to find the indices of the first $k$ people (starting from person $1$) who possess a prime number of coins. If fewer than $k$ such people exist among the first $n$ people, you should report $\{-1\}$.
## Input Format
- The first line contains two integers $n$ and $q$ ($1 \le n \le 10^9$, $1 \le q \le 1000$).
- The next $q$ lines each contain three integers $l, r, y$ ($1 \le l \le r \le n$, $0 \le y \le 10^6$). These represent the queries.
- The last line contains a single integer $k$ ($1 \le k \le 10^5$).
## Output Format
Output $k$ space-separated integers, representing the indices of the first $k$ people (in increasing order) who have a prime number of coins. If fewer than $k$ such people exist, output a single integer $-1$.
## Sample Test Cases
### Sample Input 1
```
10 2
1 3 2
2 5 3
3
```
### Sample Output 1
```
1 2 3
```
### Sample Input 2
```
5 1
1 2 1
3
```
### Sample Output 2
```
-1
```
## Constraints
- $1 \le n \le 10^9$
- $1 \le q \le 1000$
- $1 \le l \le r \le n$
- $0 \le y \le 10^6$
- $1 \le k \le 10^5$
- Time limit: 2 seconds
- Memory limit: 256 MB
## Explanation
### Sample 1:
Initially, all people have $0$ coins.
After the first query $(1, 3, 2)$, people $1, 2, 3$ each gain $2$ coins. The coin counts for people $1$ to $10$ become: $[2, 2, 2, 0, 0, 0, 0, 0, 0, 0]$.
After the second query $(2, 5, 3)$, people $2, 3, 4, 5$ each gain $3$ coins:
- Person $1$: $2$ coins.
- Person $2$: $2+3 = 5$ coins.
- Person $3$: $2+3 = 5$ coins.
- Person $4$: $0+3 = 3$ coins.
- Person $5$: $0+3 = 3$ coins.
- People $6$ to $10$: $0$ coins.
The final coin counts are: $[2, 5, 5, 3, 3, 0, 0, 0, 0, 0]$.
The prime numbers are $2, 3, 5, 7, \dots$. Note that $0$ and $1$ are not prime numbers.
People with a prime number of coins are:
- Person $1$ (has $2$ coins, which is prime)
- Person $2$ (has $5$ coins, which is prime)
- Person $3$ (has $5$ coins, which is prime)
- Person $4$ (has $3$ coins, which is prime)
- Person $5$ (has $3$ coins, which is prime)
We need to find the first $k=3$ such people. These are people $1, 2, 3$. So the output is `1 2 3`.
### Sample 2:
Initially, all people have $0$ coins.
After the query $(1, 2, 1)$, people $1, 2$ each gain $1$ coin. The coin counts for people $1$ to $5$ become: $[1, 1, 0, 0, 0]$.
Neither $0$ nor $1$ is a prime number. Thus, no people have a prime number of coins. Since $k=3$ people are requested but none exist, the output is $-1$.
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