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.