B. Array Construction
time limit per test
1 second
memory limit per test
256 megabytes
input
standard input
output
standard output

You're given three non-negative integers $$$n,x$$$ and $$$y$$$.

Determine if you can construct an array $$$a$$$ of size $$$n$$$ satisfying:

  • All elements in $$$a$$$ are distinct;
  • $$$a_1 | ... | a_n = x$$$;
  • $$$a_1 \& ... \& a_n = y$$$.

Here $$$|$$$ denotes the bitwise OR operation and $$$\&$$$ denotes the bitwise AND operation.

If you can construct such array $$$a$$$ output YES.Otherwise,output NO.

Input

Each test contains multiple test cases. The first line contains the number of test cases $$$t$$$ ($$$1 \le t \le 10^5$$$). The description of the test cases follows.

The only line of each testcase contains three integers $$$n,x,y$$$ ($$$1 \le n \le 2^{30}-1,0 \le x,y \le 2^{30}-1$$$).

Output

For each testcase output in a new line  — If you can construct such array $$$a$$$ output YES.Otherwise,output NO.

Example
Input
4
1 0 0
3 14 2
1000000000 14 2
3 6 5
Output
YES
YES
NO
NO