You are given an integer $$$n$$$. The function $$$C(i,k)$$$ represents the number of distinct ways you can select $$$k$$$ distinct numbers from the set {$$$1, 2, \ldots, i$$$} and arrange them in a circle$$$^\dagger$$$.

Find the value of $$$$$$ \sum\limits_{i=1}^n \sum\limits_{j=1}^i \left( C(i,j) \bmod j \right). $$$$$$ Here, the operation $$$x \bmod y$$$ denotes the remainder from dividing $$$x$$$ by $$$y$$$.

Since this value can be very large, find it modulo $$$10^9+7$$$.

$$$^\dagger$$$ In a circular arrangement, sequences are considered identical if one can be rotated to match the other. For instance, $$$[1, 2, 3]$$$ and $$$[2, 3, 1]$$$ are equivalent in a circle.

Input

The first line contains a single integer $$$t$$$ ($$$1 \leq t \leq 10^5$$$) — the number of test cases.

The only line of each test case contains a single integer $$$n$$$ ($$$1 \le n \le 10^6$$$).

Output

For each test case, output a single integer on a new line — the value of the expression to be calculated modulo $$$10^9+7$$$.

Note

In the first test case, $$$C(1,1) \bmod 1 = 0$$$.

In the second test case:

$$$C(1,1)=1$$$ (the arrangements are: $$$[1]$$$);
$$$C(2,1)=2$$$ (the arrangements are: $$$[1]$$$, $$$[2]$$$);
$$$C(2,2)=1$$$ (the arrangements are: $$$[1, 2]$$$);
$$$C(3,1)=3$$$ (the arrangements are: $$$[1]$$$, $$$[2]$$$, $$$[3]$$$);
$$$C(3,2)=3$$$ (the arrangements are: $$$[1, 2]$$$, $$$[2, 3]$$$, $$$[3, 1]$$$);
$$$C(3,3)=2$$$ (the arrangements are: $$$[1, 2, 3]$$$, $$$[1, 3, 2]$$$).

In total, $$$\left(C(1,1) \bmod 1\right) + \left(C(2,1) \bmod 1\right) + \left(C(2,2) \bmod 2\right) + \left(C(3,1) \bmod 1\right) + \left(C(3,2) \bmod 2\right) + \left(C(3,3) \bmod 3\right) = 4$$$.

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