Inherited disease

Jeongmin is a single-celled organism. The name JMPABU (JeongMin is Paramecium & Amoeba Based Unicellular organism) says as much: it looks like a paramecium crossed with an amoeba. I watched Jeongmin for a little over a year and found two properties.

• When a generation $D$ Jeongmin has a child, that child belongs to generation $D+1$. A generation $D$ Jeongmin leaves exactly $D+1$ children in its life, then dies.
• Jeongmin carries an unusual gene. Depending on the order in which a Jeongmin is born, that gene can be the one that causes an inherited disease.

I own a single generation 0 Jeongmin, and I numbered it 0. Its descendants get numbers too. Take the smallest-numbered Jeongmin whose children are not numbered yet, then give its children the smallest unused numbers in birth order. Repeating that produces the numbering in the picture below.

I keep running experiments on which birth order leads to the disease. The method is simple: follow the birth orders one step at a time and examine the Jeongmin you land on. For example, look at the 1st child born to the generation 0 Jeongmin, then the 2nd child born to that one, then the 1st child born to that one. Along that path the numbers you see are 1, 3 and 7, in that order. Once the generation count grows the numbers get far too large to follow by hand. I need your help.

The first line contains the generation $D$ ($1 \le D \le 100$) you want to examine.

The second line contains $D$ integers separated by spaces. The $i$-th integer $d_i$ ($1 \le d_i \le i$) means you look at the $d_i$-th child born to the generation $i-1$ Jeongmin.

Print $D$ lines. On line $k$, print the number of the generation $k$ Jeongmin you see while following the input. The number can be very large, so print it modulo 1,000,000,007.