Alice is studying the cost of packing chocolates. She has already collected and analyzed some data. Chocolates are packed in boxes that have very weird pricing: it changes as you buy more boxes. The first box one buys always costs $b_1$ burles, the second one costs $b_2$ burles and so on. Some boxes can even have negative price: meaning Alice gets the box for free and additionally gets some burles. Alice has collected the values of $b_1,b_2,...,b_n$ and wrote them down.

Next, she has also computed the sum of all possible distribution and packaging of chocolates. Specifically, for each positive integer $k$ not greater than $n$: Alice has considered all possible ways to partition $k$ chocolates of different flavors into some boxes, computed the cost of buying those boxes, and added all these costs up to obtain the total cost $a_k$. She has also written down the values of $a_1,a_2,...,a_n$. 

Getting a good night's sleep, she finds out to her horror in the morning that Wakandan spies stole her sheet containing values of $b_1,b_2,...,b_n$. So she asks for your help in recovering the values. But she does not need all the costs to complete her research, only the values of $b_l,b_{l+1},...,b_r$.

Input Format

• The first line contains a three space separated integers $n,l,r$. Here $n$ is the number of values computed by Alice, and $[l,r]$ is the range of values she asks.
• The second line contains $n$ space separated integers: the values of $a_1,a_2,...,a_n$ modulo $10^9+7$.

Constraints

• $1\le n\le 10^5$
• $1\le l\le r\le n$
• $r-l< 100$
• $0\le a_i<10^9+7$.

Output Format

• Print $r-l+1$ space separated integers: the values of $b_l,b_{l+1},...,b_r$ modulo $10^9+7$.
• It is guaranteed that the value of each $b_i$ is uniquely determined by the inputs.