gsh loves bitwise operations! Today, he is playing a game against an AI.

The rules of the game are as follows:

• gsh and the AI take turns, with gsh going first.
• They operate on two non-negative integers $a$ and $b$. gsh's goal is to transform them into the target non-negative integers $x$ and $y$, while the AI tries to prevent gsh from achieving this goal.
• On his turn, gsh can perform one of the following two operations:
  1. $a := a \& v$ (bitwise AND with some non-negative integer $v$).
  2. $b := b \mid v$ (bitwise OR with some non-negative integer $v$).
• On its turn, the AI can perform one of the following two operations:
  1. $a := a \mid v$ (bitwise OR with some non-negative integer $v$).
  2. $b := b \& v$ (bitwise AND with some non-negative integer $v$).
• The chosen $v$ must satisfy $0 \le v < 2^{60}$.
• Both sides are sufficiently intelligent and will adopt optimal strategies to win the game.
• If, within $10^{100}$ turns, there exists a moment where $a = x$ and $b = y$, then gsh wins; otherwise, the AI wins.

Determine whether gsh has a winning strategy. If he does, output Yes; otherwise, output No.

Input

The first line contains an integer $T$ ($1 \le T \le 10^5$), representing the number of test cases.

Each test case consists of a single line containing four non-negative integers $a, b, x, y$ ($0 \le a, b, x, y < 2^{60}$).

Output

For each test case, output a single line containing the string Yes or No.

Examples

Input 1

4
3 6 3 6
7 4 5 4
5 4 3 4
2 4 3 5

Output 1

Yes
Yes
No
No

Note

For the first test case, the initial state already satisfies $a = x$ and $b = y$, so gsh wins.

For the second test case, gsh performs the operation $a := a \& 5$, reaching the target, so gsh wins.

For the third and fourth test cases, it is not difficult to prove that the target can never be reached, so gsh loses.