Victor lives in a monkey country where every day, out of the $K$ monkeys who have money, the top $\lfloor {\displaystyle \frac{K\cdot P}{Q}}\rfloor$ of monkeys earn one dollar while everyone else loses one dollar. When a monkey runs out of money, he goes bankrupt and loses his citizenship too is no longer one of the $K$ monkeys with money. At first, there are $N$ monkeys and the $i^{th}$ monkey has $a_i$ dollars. Each monkey has a distinct number of dollars to begin with. Victor would like to know how many days there are until each monkey runs out of money.

Real problem statement: Victor lives in a capitalist country where every day, out of the $K$ citizens who have money, the top $\lfloor {\displaystyle \frac{K\cdot P}{Q}}\rfloor$ of citizens earn one dollar while everyone else loses one dollar. When a citizen runs out of money, he goes bankrupt and loses his citizenship too is no longer one of the $K$ citizens with money. At first, there are $N$ citizens and the $i^{th}$ citizen has $a_i$ dollars. Each citizen has a distinct number of dollars to begin with. Victor would like to know how many days there are until each citizen runs out of money.

Input Specification

The first line contains integers $N$, $P$, and $Q$ ($1\le N,P,Q\le {10}^7$, $P<Q$), the number of monkeys in the country and the special numbers $P$ and $Q$.

The next line will have a list $a$ of $N$ integers, ($1\le a_i\le {10}^9$), the $i^{th}$ of which is how many dollars the $i^{th}$ monkey has. No two monkeys have the same amount of money ($a_i\ne a_j$ if $i\ne j$). The amount of money of the monkeys are sorted in increasing order.

Output Specification

In one line, print $N$ integers, the $i^{th}$ of which is how many days there are until the $i^{th}$ monkey runs out of money modulo ${10}^9+7$.

Sample Input 1

5 1 2
1 2 3 4 5

Sample Output 1

1 2 3 8 21

Sample Input 2

2 1 2
999999999 1000000000

Sample Output 2

999999999 999999984

Explanation for Sample 1

At the start, the money count is 1 2 3 4 5.

On day 1, the top $\lfloor {\displaystyle \frac{5\cdot 1}{2}}\rfloor =2$ monkeys gain money, and everyone else loses money. Thus, the new money count becomes 0 1 2 5 6. Here, monkey 1 goes bankrupt on day 1.

The rest of the days are:

0 0 1 6 7 monkey 2 goes bankrupt on day 2.

0 0 0 5 8 monkey 3 goes bankrupt on day 3.

0 0 0 4 9

0 0 0 3 10

0 0 0 2 11

0 0 0 1 12

0 0 0 0 13 monkey 4 goes bankrupt on day 8.

0 0 0 0 12

…

0 0 0 0 1

0 0 0 0 0 The monkey game finally ends when monkey 5 goes bankrupt on day 21.