 # Good Ranges

Given a set S. A range is said to be good, if it is the largest range containing only one element.

Now, given a number A, denoting the range 1 to A, and array of B queries where each element is a query having a number X in the range 1 to A.
X is to be added to the set S.

For each query, the answer would be the sum of the upper and lower bound of the good ranges possible modulo 1000000007.

Finally, you need to return an array where element at i-th position represents the answer to i-th query.

CONSTRAINTS

``````1 <= A, size of array B <= 10^5
1 <= X <= A
``````

SAMPLE INPUT

``````A: 10
B: [2, 7, 5, 9, 6, 1, 8, 10, 3, 4]
``````

SAMPLE OUTPUT

``````[11, 20, 30, 46, 58, 61, 77, 96, 102, 110]
``````

EXPLANATION

``````First 2 is added to the set and the largest range containing only 2 is [1, 10] .

Then 7 is added and the range containing only 2 becomes [1,6] and containing only 7 becomes [3, 10].

Then 5 is added and the ranges are:

For 2 : [1,4]
For 5 : [3,6]
For 7 : [6,10]

Similarly for all other queries.
``````
NOTE: You only need to implement the given function. Do not read input, instead use the arguments to the function. Do not print the output, instead return values as specified. Still have a doubt? Checkout Sample Codes for more details. Hints
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