One day, Wet Shark was given an array $X=\{x_1,x_2,\ldots,x_m\}$. As always, he started playing with its subsequences.

When you came to know about this habit, you presented him a task of finding all pairs of subsequences, $(A,B)$, which satisfies all of the following constraints. We will represent a pair of subsequence as $A=\{x_{a_1},x_{a_2},...,x_{a_n}\}$ and $B=\{x_{b_1},x_{b_2},...,x_{b_n}\}$

$\mbox{A}$ and $\mbox{B}$ must be of same length, i.e., $|A|=|B|$.
$\sum\limits_{i=1}^{n}(x_{a_{i}}+x_{b_{i}})=r$
$\sum\limits_{i=1}^{n}(x_{a_{i}}-x_{b_{i}})=s$

Please help Wet Shark determine how many possible subsequences $\mbox{A}$ and $\mbox{B}$ can exist. Because the number of choices may be big, output your answer modulo $10^9+7=1000000007$.

Note:

Two segments are different if there's exists at least one index $\boldsymbol{i}$ such that element $x_i$ is present in exactly one of them.
Both subsequences can overlap each other.
Subsequences do not necessarily have to be distinct

Input Format

The first line consists of 3 space-separated integers $m$, $\textbf{r}$, $\boldsymbol{\mathrm{~S~}}$, where $m$ denotes the length of the original array, $\mbox{X}$, and $\textbf{r}$ and $\boldsymbol{\mathrm{~S~}}$ are as defined above.

The next line contains $m$ space-separated integers, $x_1,x_2,\ldots,x_m$ , representing the elements of $\mbox{X}$.

Constraints

$1\leq m\leq100$
$0\leq r,\:\textit{s}\leq2000$
$1\leq x_i\leq2000$

Output Format

Output total number of pairs of subsequences, $(A,B)$, satisfying the above conditions. As the number can be large, output it's modulo $10^9+7=1000000007$

Sample Input 0
4 5 3
1 1 1 4

Sample Output 0
3

Explanation 0

For array $X=\{x_1,x_2,x_3,x_4\}=\{1,1,1,4\}$ there are three pairs of subsequences:

$A=\{x_4\}=\{4\};B=\{x_1\}=\{1\}$
$A=\{x_4\}=\{4\};B=\{x_2\}=\{1\}$
$A=\{x_4\}=\{4\};B=\{x_3\}=\{1\}$

见题面

见题面