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F. Rainbow Balls

time limit per test

2 secondsmemory limit per test

256 megabytesinput

standard inputoutput

standard outputYou have a bag of balls of *n* different colors. You have *a*_{i} balls of the *i*-th color.

While there are at least two different colored balls in the bag, perform the following steps:

- Take out two random balls without replacement one by one. These balls might be the same color.
- Color the second ball to the color of the first ball. You are not allowed to switch the order of the balls in this step.
- Place both balls back in the bag.
- All these actions take exactly one second.

Let *M* = 10^{9} + 7. It can be proven that the expected amount of time needed before you stop can be represented as a rational number , where *P* and *Q* are coprime integers and where *Q* is not divisible by *M*. Return the value .

Input

The first line of input will contain a single integer *n* (1 ≤ *n* ≤ 2 500) — the number of colors.

The next line of input will contain *n* space separated integers *a*_{1}, *a*_{2}, ..., *a*_{n} (1 ≤ *a*_{i} ≤ 10^{5}) — the number of balls of each color.

Output

Print a single integer, the answer to the problem.

Examples

Input

2

1 1

Output

1

Input

3

1 2 3

Output

750000026

Note

In the first sample, no matter what happens, the balls will become the same color after one step.

For the second sample, we have 6 balls. Let’s label the balls from 1 to 6, and without loss of generality, let’s say balls 1,2,3 are initially color 1, balls 4,5 are color 2, and ball 6 are color 3.

Here is an example of how these steps can go:

- We choose ball 5 and ball 6. Ball 6 then becomes color 2.
- We choose ball 4 and ball 5. Ball 5 remains the same color (color 2).
- We choose ball 1 and ball 5. Ball 5 becomes color 1.
- We choose ball 6 and ball 5. Ball 5 becomes color 2.
- We choose ball 3 and ball 4. Ball 4 becomes color 1.
- We choose ball 4 and ball 6. Ball 6 becomes color 1.
- We choose ball 2 and ball 5. Ball 5 becomes color 1.

It can be shown that the answer to this case is .

Codeforces (c) Copyright 2010-2018 Mike Mirzayanov

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