Final Standings

문제

Formula TheByte is the most famous race competition in ByteLand. The competition is over and each of n drivers has a number of points. A driver that has more points is placed higher.

Final standings are not disclosed yet, but we know that the total number of points earned by all the drivers is p and there are only d different numbers of points among top k drivers.

The ByteLand Times asks you to guess final standings based on the given information.

입력

The only line of the input file contains four integer numbers: n, p, k and d — the number of drivers, the number of points, the number of top drivers, and the number of different numbers of points among top k drivers (1 ≤ k ≤ n ≤ 1000; 0 ≤ p ≤ 1 000 000; 1 ≤ d ≤ k).

출력

Output the possible standings that match given n, p, k and d.

If it is possible to create the correct final standings, you should output final standings. The i-th line of the final standings must contain a number of points earned by i-th driver. Drivers should be ordered by number of points in the descending order.

If there is no possible final standings satisfying the given data, output the single line “Wrong information”.

3 4 2 2

2
1
1

3 5 2 2

3
2
0

2 5 2 1

Wrong information