Remove a Single Element 2
Given a list of
n integers, you are asked to remove one of the integers in a way that the product of the resulting sequence modulo m is equal to p. More formally, if the index of the removed element is r:The program should find the index of that number or print
Impossible if that kind of number does not exist.Input
The first line of the input contains 3 integers
n (1 ≤ n ≤ ), m (1 ≤ m ≤ ), and p (0 ≤ s < m).The second line contains
n space-separated integers Output
In case such a number does not exist, the program should print
Impossible, otherwise, the program should print the smallest index of such a number in the given sequence. The indexing starts from 1.Examples
Input | Output |
3 8 5
5 0 9 | 2 |
3 8 5
5 10 7 | Impossible |
Explanation
- 5 * 9 = 45 ⇒ 45 mod 8 = 5 ⇒ we can remove the element with value 0 at position 2.
- It’s not possible to remove any of the elements to turn the product of the resulting array modulo 8 to be equal to 5.
Constraints
Time limit: 2 seconds
Memory limit: 512 MB
Output limit: 1 MB