# Binary Sequence

## Problem:-

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.

When x, y, a and b are 3, 2, 4 and 2 respectively, string 00110 is a valid string. So answer is Yes

When x, y, a and b are 3, 3, 4 and 3 respectively, we can’t find any valid string. So answer is No.