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bitmasks

brute force

math

*1800

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E. Apollo versus Pan

time limit per test

2 secondsmemory limit per test

256 megabytesinput

standard inputoutput

standard outputOnly a few know that Pan and Apollo weren't only battling for the title of the GOAT musician. A few millenniums later, they also challenged each other in math (or rather in fast calculations). The task they got to solve is the following:

Let $$$x_1, x_2, \ldots, x_n$$$ be the sequence of $$$n$$$ non-negative integers. Find this value: $$$$$$\sum_{i=1}^n \sum_{j=1}^n \sum_{k=1}^n (x_i \, \& \, x_j) \cdot (x_j \, | \, x_k)$$$$$$

Here $$$\&$$$ denotes the bitwise and, and $$$|$$$ denotes the bitwise or.

Pan and Apollo could solve this in a few seconds. Can you do it too? For convenience, find the answer modulo $$$10^9 + 7$$$.

Input

The first line of the input contains a single integer $$$t$$$ ($$$1 \leq t \leq 1\,000$$$) denoting the number of test cases, then $$$t$$$ test cases follow.

The first line of each test case consists of a single integer $$$n$$$ ($$$1 \leq n \leq 5 \cdot 10^5$$$), the length of the sequence. The second one contains $$$n$$$ non-negative integers $$$x_1, x_2, \ldots, x_n$$$ ($$$0 \leq x_i < 2^{60}$$$), elements of the sequence.

The sum of $$$n$$$ over all test cases will not exceed $$$5 \cdot 10^5$$$.

Output

Print $$$t$$$ lines. The $$$i$$$-th line should contain the answer to the $$$i$$$-th text case.

Example

Input

8 2 1 7 3 1 2 4 4 5 5 5 5 5 6 2 2 1 0 1 0 1 1 6 1 12 123 1234 12345 123456 5 536870912 536870911 1152921504606846975 1152921504606846974 1152921504606846973

Output

128 91 1600 505 0 1 502811676 264880351

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