Andi is a mathematician, a computer scientist, and a songwriter. After spending so much time writing songs, he finally writes a catchy melody that he thought as his best creation. However, the singer who will sing the song/melody has a unique vocal range, thus, an adjustment may be needed.

A melody is defined as a sequence of N notes which are represented by integers. Let A be the original melody written by Andi. Andi needs to adjust A into a new melody B such that for every i where 1 ≤ i < N: 

  * If A_i < A_{i+1}, then B_i < B_{i+1}. 
  * If A_i = A_{i+1}, then B_i = B_{i+1}. 
  * If A_i > A_{i+1}, then B_i > B_{i+1}. 
  * |B_i - B_{i+1}| ≤ K, i.e. the difference between two successive notes is no larger than K. 

Moreover, the singer also requires that all notes are within her vocal range, i.e. L ≤ B_i ≤ R for all 1 ≤ i ≤ N.

Help Andi to determine whether such B exists, and find the lexicographically smallest B if it exists. A melody X is lexicographically smaller than melody Y if and only if there exists j (1 ≤ j ≤ N) such that X_i = Y_i for all i < j and X_{j} < Y_{j}.

For example, consider a melody A = \{1,3,5,6,7,8,9,10,3,7,8,9,10,11,12,12\} as shown in the following figure. The diagonal arrow up in the figure implies that A_i < A_{i+1}, the straight right arrow implies that A_i = A_{i+1}, and the diagonal arrow down implies that A_i > A_{i+1}.

<image>

Supposed we want to make a new melody with L = 1, R = 8, and K = 6. The new melody B = \{1,2,3,4,5,6,7,8,2,3,4,5,6,7,8,8\} as shown in the figure satisfies all the requirements, and it is the lexicographically smallest possible.

Input

Input begins with a line containing four integers: N L R K (1 ≤ N ≤ 100 000; 1 ≤ L ≤ R ≤ 10^9; 1 ≤ K ≤ 10^9) representing the number of notes in the melody, the vocal range (L and R), and the maximum difference between two successive notes in the new melody, respectively. The next line contains N integers: A_i (1 ≤ A_i ≤ 10^9) representing the original melody.

Output

Output in a line N integers (each separated by a single space) representing the lexicographically smallest melody satisfying all the requirements, or output -1 if there is no melody satisfying all the requirements. Note that it might be possible that the lexicographically smallest melody which satisfies all the requirements to be the same as the original melody.

Examples

Input


16 1 8 6
1 3 5 6 7 8 9 10 3 7 8 9 10 11 12 12


Output


1 2 3 4 5 6 7 8 2 3 4 5 6 7 8 8


Input


16 1 8 6
1 3 5 6 7 8 9 10 3 7 8 9 10 11 12 13


Output


-1


Input


16 1 10 10
1 3 5 6 7 8 9 10 3 7 8 9 1 11 12 13


Output


1 2 3 4 5 6 7 8 1 2 3 4 1 2 3 4

Note

Explanation for the sample input/output #1

This is the example from the problem description.

Source: codeforces | Difficulty: HARD
Tags: Amortized analysis

Greedy algorithms


Solutions: