This is the hard version of the problem. The difference between the versions is that in this version, $l\le r$. You can hack only if you solved all versions of this problem.

You are given a positive integer $n$ and the first $n$ terms of an infinite binary sequence $a$, which is defined as follows:

• For $m \gt n$, $a_m = a_1 \oplus a_2 \oplus \ldots \oplus a_{\lfloor \frac{m}{2} \rfloor}$$^{\text{∗}}$.

Your task is to compute the sum of elements in a given range $[l, r]$: $a_l + a_{l + 1} + \ldots + a_r$.

$^{\text{∗}}$$\oplus$ denotes the bitwise XOR operation.

Input

Each test contains multiple test cases. The first line contains the number of test cases $t$ ($1 \le t \le 10^4$). The description of the test cases follows.

The first line of each test case contains three integers $n$, $l$, and $r$ ($1 \le n \le 2 \cdot 10^5$, $1 \le l \leq r \le 10^{18}$).

The second line contains $n$ integers $a_1, a_2, \ldots, a_n$ ($\color{red}{a_i \in \{0, 1\}}$) — the first $n$ terms of the sequence $a$.

It is guaranteed that the sum of $n$ over all test cases does not exceed $2 \cdot 10^5$.

Output

For each test case, output a single integer — the sum of elements in the given range.

Note

In the first test case, the sequence $a$ is equal to $$[\underline{\color{red}{1}}, 1, 1, 0, 0, 1, 1, 1, 1, 1, \ldots]$$ where $l = 1$, and $r = 1$. The sum of elements in the range $[1, 1]$ is equal to $$a_1 = 1.$$

In the second test case, the sequence $a$ is equal to $$[\color{red}{1}, \color{red}{0}, \underline{1, 1, 1, 0, 0, 1, 1, 0}, \ldots]$$ where $l = 3$, and $r = 10$. The sum of elements in the range $[3, 10]$ is equal to $$a_3 + a_4 + \ldots + a_{10} = 1 + 1 + 1 + 0 + 0 + 1 + 1 + 0 = 5.$$