Primes and XOR? Nonsense

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 $\mathbb{P}\_{LR}$.

The 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 $R$ ($2 \le L \le R \le 10^{12}$).

For each test case print the answer on a separate line.

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.