Background

Xiaoka has recently become obsessed with prime numbers, so he came up with a problem related to primes to test you.

A prime number is a natural number greater than $1$ that has no divisors other than $1$ and itself.

Problem Description

Xiaoka has $T(1\le T\le 10^5)$ queries. In each query, you are given two positive integers $x,y(1\le x,y\le 10^9)$.

Xiaoka wants to know whether the $x$-th prime number and the $y$-th prime number satisfy $p_x \oplus p_y = 1$, that is, whether the XOR value of the $x$-th prime and the $y$-th prime is $1$.

Input Format

The first line contains a positive integer $T$, representing the number of queries.

The next $T$ lines each contain two positive integers $x,y$, representing a query about the $x$-th prime number and the $y$-th prime number.

Output Format

Output $T$ lines. Each line contains a string Yes or No, indicating whether the XOR value of the two prime numbers is $1$ or not $1$, respectively.

4
1 2
23 145
66 2
1 14

Yes
No
No
No

Hint

Translated by ChatGPT 5