Tenzing has an array $a$ of length $n$ and an integer $v$.

Tenzing will perform the following operation $m$ times:

1. Choose an integer $i$ such that $1 \leq i \leq n$ uniformly at random.
2. For all $j$ such that $i \leq j \leq n$, set $a_j := a_j + v$.

Tenzing wants to know the expected value of $\prod_{i=1}^n a_i$ after performing the $m$ operations, modulo $10^9+7$.

Formally, let $M = 10^9+7$. It can be shown that the answer can be expressed as an irreducible fraction $\frac{p}{q}$, where $p$ and $q$ are integers and $q \not \equiv 0 \pmod{M}$. Output the integer equal to $p \cdot q^{-1} \bmod M$. In other words, output the integer $x$ that $0 \le x < M$ and $x \cdot q \equiv p \pmod{M}$.

The first line of input contains three integers $n$, $m$ and $v$ ($1\leq n\leq 5000$, $1\leq m,v\leq 10^9$).

The second line of input contains $n$ integers $a_1,a_2,\ldots,a_n$ ($1\leq a_i\leq 10^9$).

Output the expected value of $\prod_{i=1}^n a_i$ modulo $10^9+7$.