Problem Statement

The Republic of ARC has $N$ citizens, all of whom play competitive programming. Each citizen is given a dan (grade) which is $1$, $2$, $\ldots$, or $K$, according to their skill.

A national census has revealed that there are exactly $A_i$ citizens with dan $i$. To make this data easier to understand, the king has decided to describe the country as if it were a village of $M$ people.

Set the number of people with dan $i$ in the village, $B_i$, so that $\max_i\left|\frac{B_i}{M} - \frac{A_i}{N}\right|$ is minimized, while satisfying the following:

• each $B_i$ is a non-negative integer, satisfying $\sum_{i=1}^K B_i = M$.

Print one such way to set $B = (B_1, B_2, \ldots, B_K)$.

Constraints

• $1\leq K\leq 10^5$
• $1\leq N, M\leq 10^9$
• Each $A_i$ is a non-negative integer satisfying $\sum_{i=1}^K A_i = N$.

Input

Input is given from Standard Input in the following format:

K N M
A_1 A_2 \ldots A_K

Output

Print the elements in your integer sequence $B$ satisfying the requirement in one line, with spaces in between.

B_1 B_2 \ldots B_K

If multiple sequences satisfy the requirement, any of them will be accepted.