409120: GYM103439 L Primes and XOR? Nonsense
Description
Define $$$\mathbb{P}_{LR} = \mathbb{P} \cap [L;R]$$$, where $$$\mathbb{P}$$$ is the set of prime numbers. In other words, $$$\mathbb{P}_{LR}$$$ is the set of all primes between $$$L$$$ and $$$R$$$ inclusive.
Given $$$L$$$ and $$$R$$$, find the number of integers that can be represented as XOR of some (possibly empty) subset of $$$\mathbb{P}_{LR}$$$.
InputThe first line of input contains one integer $$$T$$$ ($$$1 \le T \le 100$$$) — the number of independent test cases you need to process. Descriptions of $$$T$$$ test cases follow.
The description of one test case consists of two integers $$$L$$$ and $$$R$$$ ($$$2 \le L \le R \le 10^{12}$$$).
OutputFor each test case print the answer on a separate line.
ExampleInput3 2 10 999999940 1000000000 2 1000000000000Output
8 1 1099511627776Note
In the first example, $$$\mathbb{P}_{LR} = \{ 2, 3, 5, 7 \}$$$.
- $$$0 = 2 \oplus 5 \oplus 7$$$
- $$$1 = 2 \oplus 3$$$
- $$$2 = 2$$$
- $$$3 = 3$$$
- $$$4 = 3 \oplus 7$$$
- $$$5 = 2 \oplus 7$$$
- $$$6 = 3 \oplus 5$$$
- $$$7 = 7$$$
In the second example, $$$\mathbb{P}_{LR} = \varnothing$$$, so only $$$0$$$ can be represented as XOR of some subset.