Given four integers $$x, y, a$$ and $$b$$. Determine if there exists a binary string having $$x$$ 0's and $$y$$ 1's such that the total number of subsequences equal to the sequence "01" in it is $$a$$ and the total number of subsequences equal to the sequence "10" in it is $$b$$.

A binary string is a string made of the characters '0' and '1' only.

A sequence $$a$$ is a subsequence of a sequence $$b$$ if $$a$$ can be obtained from $$b$$ by deletion of several (possibly, zero or all) elements.

Input Format

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

Each of the next $$T$$ lines contains four integers $$x$$, $$y$$, $$a$$ and $$b$$ (($$1 \le x, y \le 10^5$$, ($$0 \le a, b \le 10^9$$)), as described in the problem.

Output Format

For each test case, output "Yes'' (without quotes) if a string with given conditions exists and "No'' (without quotes) otherwise.