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