CF2180E.No Effect XOR

In the jungle, there is a lake with infinite lily pads on it. The lily pads are numbered with non-negative integers $0, 1, 2, 3, \ldots$. The lily pads with numbers between $l$ and $r$ inclusive are called suitable, while all other lily pads are not suitable for the frogs to sit on.

Currently, a single frog is sitting on each suitable lily pad.

Ostad is watching the lake and wants to reorder the frogs. To do so, Ostad can pick a positive integer $x$ and announce it to the frogs. After hearing the number, the frog sitting on the $i$-th lily pad will jump to the $(i \oplus x)$-th one, where $\oplus$ denotes the bitwise XOR operation.

Ostad likes the frogs, and therefore he wants to pick the number $x$ in such a way that all frogs stay within the range of suitable lily pads.

Help Ostad by counting how many different numbers $x$ Ostad can choose such that no frog jumps outside the suitable segment of the lily pads.

在丛林中，有一片湖泊，湖面上有无数片睡莲叶。这些睡莲叶按非负整数编号：$0, 1, 2, 3, \ldots$。编号在区间 $[l, r]$（含端点）内的睡莲叶被称为“合适”的，其余所有睡莲叶则不适合青蛙落坐。

目前，每片“合适”的睡莲叶上恰好坐着一只青蛙。

Ostad 正在观察这片湖泊，并希望重新安排这些青蛙的位置。为此，Ostad 可以选择一个正整数 $x$ 并向所有青蛙宣布该数。听到该数后，坐在第 $i$ 片睡莲叶上的青蛙将跳到第 $(i \oplus x)$ 片睡莲叶上，其中 $\oplus$ 表示按位异或运算。

Ostad 喜欢这些青蛙，因此他希望选择的 $x$ 满足：所有青蛙跳跃后仍落在“合适”的睡莲叶范围内（即仍在区间 $[l, r]$ 内）。

请帮助 Ostad 计算：有多少个不同的正整数 $x$ 满足上述条件？

Each test contains multiple test cases. The first line contains the number of test cases $t$ ($1 \le t \le 10^5$). The description of the test cases follows.

For each test case, there is a single line containing two integers $l$ and $r$ ($1 \leq l \leq r \leq 10^{15}$).

每个测试包含多个测试用例。第一行包含测试用例的数量 $t$（$1 \le t \le 10^5$）。随后是测试用例的描述。

对于每个测试用例，有一行包含两个整数 $l$ 和 $r$（$1 \leq l \leq r \leq 10^{15}$）。

For each test case, output a single integer denoting the number of valid values for $x$.

对于每个测试用例，输出一个整数，表示满足条件的 $x$ 的取值个数。

In the first test case, $x = 3$ is the only number that Ostad can choose, as $1 \oplus 3 = 2$ and $2 \oplus 3 = 1$, which are within the range $[1, 2]$.

There are no valid choices for Ostad in the second and third test cases. For the second case, since we require $x \gt 0$, the only frog that we have will leave the range. Similarly, in the third case, no valid $x$ exists to keep the frogs within the desired range.

In the fourth test case, Ostad can choose $1$, $2$, or $3$.

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在第一个测试用例中，$x = 3$ 是 Ostad 唯一可选的数，因为 $1 \oplus 3 = 2$ 且 $2 \oplus 3 = 1$，结果均在区间 $[1, 2]$ 内。

在第二个和第三个测试用例中，Ostad 没有合法的选择。对于第二个用例，由于要求 $x \gt 0$，我们唯一的一只青蛙将离开该区间。类似地，在第三个用例中，不存在任何合法的 $x$ 能使所有青蛙保持在目标区间内。

在第四个测试用例中，Ostad 可以选择 $1$、$2$ 或 $3$。

可视化工具链接