This year METU CClub Programming Contest has attracted \(N\) participants. Each contestant has a rating which is always a positive integer. Let's denote the participant ratings with \(R_1, R_2, ... ,R_N\). It's known that the maximal rating is \(Max\), the minimal rating is \(Min\) and the average rating is \(Mean\) where:

• \(Max = max (R_1,R_2,...,R_N)\)
• \(Min = min (R_1,R_2,...,R_N)\)
• \(Mean = (R_1+R_2+...+R_N)/N\)

Your task is to find any possible set of METU CClub Programming Contest participant ratings.

Input

Four integers \(N\), \(Max\), \(Min\) and \(Mean\) separated with single spaces.

Output

Print \(N\) positive integers \(R_1, R_2, ... ,R_N\) separated with single spaces. If there are multiple solutions print any of them. If there is no solution print "Impossible" (quotes for clarity) instead.

Constraints

• \(1 ≤ N ≤ 100\)
• \(1 ≤ Min ≤ Mean ≤ Max ≤ 10000\)

Examples

Input (stdin)

4 2000 1000 1400
4 2000 1000 1800

Output(stdout)

1600 1000 2000 1000
Impossible

Notes

In the first sample there are multiple solutions, for instance:

• 1000 1275 1325 2000
• 2000 1000 1599 1001