Arithmetic Progression Subsequences (1) X57357

Statement

Write a program that reads two integers $n$ and $r$ , both strictly greater than $1$ , followed by a sequence of integers, and finds out whether the sequence contains a consecutive subsequence of length at least $n$ that forms an arithmetic progression with step $r$ .

A consecutive subsequence of integers forms an arithmetic progression with step $r$ if the difference between two consecutive numbers equals $r$ . For instance, $4 5 6 7$ is an arithmetic progression with $r = 1$ , and $22 33 44 55 66$ is an arithmetic progression with $r = 11$ .

If the input sequence contains such a progression, the program must print a line with the first $n$ elements in the progression. Otherwise, the program must indicate "No arithmetic progression found with step r and length at least n".

Input

The input consists of two integers $n>1$ and $r>1$ , followed by a sequence of integers containing at least 2 elements.

Output

If a progression subsequence with reason $r$ and length at least $n$ exists, the output are the first $n$ elements of the progression. Otherwise, the output is "No arithmetic progression found with step r and length at least n".

Public test cases

Input

4 1
7 1 -2 6 9 10 11 12 15

Output

9 10 11 12

Input

4 1
7 1 -2 5 6 7 8 9 12 15

Output

5 6 7 8

Input

Output

10 21 32 43 54

Input

5 3
2 4 6 8 10 12 14 21

Output

No arithmetic progression found with step 3 and length at least 5

Input

5 3
7 1  2 5 8 11
32 43 54 
88 3 -5 -6

Output

No arithmetic progression found with step 3 and length at least 5

Information

Author: ProAl
Language: English
Official solutions: Python
User solutions: Python