Description

We are given a sequence of N positive integers a = [a1, a2, ..., aN] on which we can perform contraction operations.

One contraction operation consists of replacing adjacent elements ai and ai+1 by their difference ai-a_i+1. For a sequence of N integers, we can perform exactly N-1 different contraction operations, each of which results in a new (N-1) element sequence.

Precisely, let con(a,i) denote the (N-1) element sequence obtained from [a1, a2, ..., aN] by replacing the elements ai and a_i+1 by a single integer ai-a_i+1 :

con(a,i) = [a1, ..., ai-1, ai-a_i+1, a_i+2, ..., aN]

Applying N-1 contractions to any given sequence of N integers obviously yields a single integer.

For example, applying contractions 2, 3, 2 and 1 in that order to the sequence [12,10,4,3,5] yields 4, since :

con([12,10,4,3,5],2) = [12,6,3,5]
con([12,6,3,5]   ,3) = [12,6,-2]
con([12,6,-2]    ,2) = [12,8]
con([12,8]       ,1) = [4]

Given a sequence a1, a2, ..., aN and a target number T, the problem is to find a sequence of N-1 contractions that applied to the original sequence yields T.

Input

The first line of the input contains two integers separated by blank character : the integer N, 1 <= N <= 100, the number of integers in the original sequence, and the target integer T, -10000 <= T <= 10000.

The following N lines contain the starting sequence : for each i, 1 <= i <= N, the (i+1)^st line of the input file contains integer ai, 1 <= ai <= 100.

Output

Output should contain N-1 lines, describing a sequence of contractions that transforms the original sequence into a single element sequence containing only number T. The ith line of the output file should contain a single integer denoting the i^th contraction to be applied.

You can assume that at least one such sequence of contractions will exist for a given input.

5 4
12
10
4
3
5

2
3
2
1

Source

CEOI 1998