A false witness that speaketh lies!

You are given a sequence containing n integers. There is a variable res that is equal to 0 initially. The following process repeats k times.

Choose an index from 1 to n uniformly at random. Name it x. Add to res the multiply of all a_i's such that 1 ≤ i ≤ n, but i ≠ x. Then, subtract a_x by 1.

You have to find expected value of res at the end of the process. It can be proved that the expected value of res can be represented as an irreducible fraction $\text{[math]}$ . You have to find $\text{[math]}$ .

Input

The first line contains two integers n and k (1 ≤ n ≤ 5000, 1 ≤ k ≤ 10⁹) — the number of elements and parameter k that is specified in the statement.

The second line contains n space separated integers a₁, a₂, ..., a_n (0 ≤ a_i ≤ 10⁹).

Output

Output a single integer — the value $\text{[math]}$ .

Lust

Examples