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F. Rainbow Balls
time limit per test
2 seconds
memory limit per test
256 megabytes
input
standard input
output
standard output

You have a bag of balls of n different colors. You have ai 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 = 109 + 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 a1, a2, ..., an (1 ≤ ai ≤ 105) — 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.
At this point, the game ends since all the balls are the same color. This particular sequence took 7 seconds.

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