Orig Description
Score : 300 points
Problem StatementThere is a box containing N balls. The i-th ball has the integer A_i written on it.
Snuke can perform the following operation any number of times:
Take out two balls from the box. Then, return them to the box along with a new ball, on which the absolute difference of the integers written on the two balls is written.
Determine whether it is possible for Snuke to reach the state where the box contains a ball on which the integer K is written.
Constraints
1 \leq N \leq 10^5
1 \leq A_i \leq 10^9
1 \leq K \leq 10^9
All input values are integers.
InputInput is given from Standard Input in the following format:
N K
A_1 A_2 ... A_N
OutputIf it is possible for Snuke to reach the state where the box contains a ball on which the integer K is written, print POSSIBLE; if it is not possible, print IMPOSSIBLE.
Sample Input 13 7
9 3 4
Sample Output 1POSSIBLE
First, take out the two balls 9 and 4, and return them back along with a new ball, abs(9-4)=5.
Next, take out 3 and 5, and return them back along with abs(3-5)=2.
Finally, take out 9 and 2, and return them back along with abs(9-2)=7.
Now we have 7 in the box, and the answer is therefore POSSIBLE.
Sample Input 23 5
6 9 3
Sample Output 2IMPOSSIBLE
No matter what we do, it is not possible to have 5 in the box. The answer is therefore IMPOSSIBLE.
Sample Input 34 11
11 3 7 15
Sample Output 3POSSIBLE
The box already contains 11 before we do anything. The answer is therefore POSSIBLE.
Sample Input 45 12
10 2 8 6 4
Sample Output 4IMPOSSIBLE
Extracted Specification
An integer N (1 ≤ N ≤ 10^5), representing some quantity or size.
An integer K (1 ≤ K ≤ 10^9), representing some target or specific value.
A list of integers A of size N, where each integer is between 1 and 1e9.
### Example Input:
```
3 7
9 3 4
```
### Function Signature:
Write a function f(N, K, A) that takes in the input.
def f(N: int, K: int, A: List[int]):
'''
N: an integer
K: an integer
A: a list of integers
'''
Test Case Generator
Sure, here is a test case generator for the given problem statement:
```python
import random
def tcgen():
# Constraint values
N_max = 10**5
A_max = 10**9
K_max = 10**9
# Generate N
N = random.randint(1, N_max)
# Generate K
K = random.randint(1, K_max)
# Generate array A of size N with values between 1 and A_max
A = [random.randint(1, A_max) for _ in range(N)]
return N, K, A
# Function to print the test case in the required format
def format_test_case(N, K, A):
print(N, K)
print(' '.join(map(str, A)))
# Generate a test case
N, K, A = tcgen()
# Print the test case
format_test_case(N, K, A)
```
This code will generate a random valid test case for the given problem. The `tcgen` function generates values for \(N\), \(K\), and the array \(A\) based on the constraints provided. The `format_test_case` function prints the generated test case in the required input format.
Here is how you can use it:
1. Call `tcgen()` to generate a test case.
2. Use `format_test_case(N, K, A)` to print the generated test case.
Example usage:
```python
N, K, A = tcgen()
format_test_case(N, K, A)
```
It will print something like:
```
92345 987654321
123456789 987654321 123456789 987654321 ... (up to 92345 numbers)
```
This ensures that the test cases are generated within the constraints provided for the problem.
Extract Arguments
def extract_arguments(fh):
N, K = map(int, fh.readline().strip().split())
A = list(map(int, fh.readline().strip().split()))
return N, K, A