Problem Statement

You have $n$ lights numbered from $1$ to $n$, and initially, all of them are turned off.

Each light has two states: on or off. Each time you press a light's switch, its state will change. If it was on, it will turn off; if it was off, it will turn on.

You plan to start from light $1$ and press each light's switch sequentially.

When pressing the switch for the $i$-th light, the following rules are executed in order:

1. The state of the $i$-th light changes.
2. You will also press the switches of lights numbered $2i, 3i, \dots$ in sequence, and their states will also change. (These operations are also considered pressing a light switch and will trigger the two rules, causing a chain reaction)

Given multiple test cases, each containing two integers $n$ and $k$, you need to determine whether the $k$-th light is on or off after completing the above process.

Input Format

The first line contains a positive integer $T$, indicating there are $T$ test cases ($1 \leq T \leq 10^5$).

The next $T$ lines each contain two integers $n$ and $k$, indicating whether the $k$-th light is on after operating on $n$ lights ($1 \leq k \leq n \leq 10^6$).

Output Format

Output $T$ lines, each with the result. For each test case, if the $k$-th light is on, output YES; otherwise, output NO.

The output can be in any case-insensitive form (e.g., "yEs", "yes", "Yes", and "YES" are all acceptable).

Sample #1

Sample Input #1

2
1 1
3 2

Sample Output #1

YES
NO

Hints

• For the example with $T=2$:
  • When $n=1$, there is only one light. After pressing it, the light is on, so the output is YES.
  • When $n=3$, after pressing light $1$, you need to press lights $2$ and $3$. Then you press light $2$. Finally, light $2$ is off, so the output is NO.