Background

Ai likes numbers.

She also likes transformations.

Problem Description

There is an integer $a$ that starts as $1$.

Ai wants $a$ to undergo exactly $k$ transformations. Each time, she chooses one of the following two transformations:

• $a \gets a - 1$;
• $a \gets a \times 2$.

Ai is curious whether, after exactly $k$ transformations, $a$ can become $n$.

Input Format

This problem contains multiple test cases.

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

The next $T$ lines each contain two integers, in order $k$ and $n$, representing one query from Ai.

Output Format

Output $T$ lines. For each query, if $a$ can become $n$, output Yes; otherwise output No.

3
2 5
2 4
3 3

No
Yes
Yes

5
4 869
48 69
8 328
66 114514
168 1919810

No
Yes
No
Yes
Yes

Hint

Sample Explanation 1

• If $k = 2$ and $n = 5$, it can be proven that there is no solution.
• If $k = 2$ and $n = 4$, one possible sequence of operations is:
  • Step 1: $a \gets a\times 2 = 2$;
  • Step 2: $a \gets a\times 2 = 4$.
• If $k = 3$ and $n = 3$, one possible sequence of operations is:
  • Step 1: $a \gets a\times 2 = 2$;
  • Step 2: $a \gets a\times 2 = 4$.
  • Step 3: $a \gets a-1 = 3$.

Constraints

This problem uses bundled testdata.

• Subtask 0 (10 pts): $T \leq 10$, $k \leq 15$.
• Subtask 1 (25 pts): $n, k \leq 2\times 10^3$.
• Subtask 2 (65 pts): No special constraints.

For all testdata, $1 \leq T \leq 10^5$, $0 \leq n, k \leq 10^{18}$.

Translated by ChatGPT 5