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Chiaki Sequence Reloaded

[编程题]Chiaki Sequence Reloaded
Chiaki is interested in an infinite sequence a1, a2, a3, ..., which defined as follows:

Chiaki would like to know the sum of the first n terms of the sequence, i.e. . As this number may be very large, Chiaki is only interested in its remainder modulo (109 + 7).

输入描述:
There are multiple test cases. The first line of input contains an integer T (1 ≤ T ≤ 105), indicating the number of test cases. For each test case:
The first line contains an integer n (1 ≤ n ≤ 1018).


输出描述:
For each test case, output an integer denoting the answer.
示例1

输入

10
1
2
3
4
5
6
7
8
9
10

输出

0
1
2
2
4
4
6
7
8
11

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