All Tracks Python Getting Started Numbers Problem

Binary Sequence
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Ad-Hoc, Getting Started, Number, Python

Problem
Editorial
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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.

SAMPLE INPUT
3
3 2 4 2
3 3 6 3
3 3 4 3
SAMPLE OUTPUT
Yes
Yes
No
Explanation

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.

 

Time Limit: 2.0 sec(s) for each input file.
Memory Limit: 256 MB
Source Limit: 1024 KB

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