A Triangle and Two Squares
All submissions for this problem are available.You are given two squares A and B. The square A has a side length of $a$ and B has a side length of $b$. The left-bottom point of square A is at $(0, 0)$ and the top-right at $(a, a)$. Square B's left-bottom point is $(x, y)$ and top-right is $(x + b, y + b)$. It's guaranteed that square B lies inside square A (may not be strictly inside, can touch too). In other words, $0 \leq x, 0 \leq y, (x + b \leq a, y + b \leq a)$. You have to tell whether you can construct a triangle T such that - All the vertices of the triangle lie on the boundary of square A. - One of its sides is parallel to one of the sides of the square A and this side should contain one of the sides of square B as a subsegment. That is, there should be a side of the triangle, say $T_2T_3$, which is parallel to one of the sides of square A, and which contains a side of square B, say $Q_3Q_4$. That is, the line segment $Q_3Q_4$ should lie within the line segment $T_2T_3$. - Square B is inside the triangle T (is allowed to touch the sides of T, but shouldn’t go outside the triangle T) ### Input - The first line of the input contains an integer $T$ denoting the number of test cases. The description of the test cases follows. - The first line of each test case contains four space-separated integers $a, b, x, y$. ### Output For each test case, print a single line containing the string `yes` if it is possible to construct such a triangle, or `no` if it is impossible. ###Constraints - $1 \le T \le 10^5$ - $1 \le b \leq a \le 10000$ - $0 \le x, y \le a - b$ ### Example Input ``` 4 4 1 1 2 3 1 1 2 3 1 0 0 3 2 1 1 ``` ### Example Output ``` yes yes yes no ``` ###Explanation **Testcase 1**: The following figure shows one possible way in which the triangle can be constructed: ![Testcase 2](https://codechef_shared.s3.amazonaws.com/download/Images/TST18KGP/SQRTRI... =475x475) Square A is P1 P2 P3 P4, square B is Q1 Q2 Q3 Q4 and the constructed triangle T is T1 T2 T3. **Testcase 2**: The following figure shows one possible way in which the triangle can be constructed: ![Testcase 2](https://codechef_shared.s3.amazonaws.com/download/Images/TST18KGP/SQRTRI... =475x475) Square A is P1 P2 P3 P4, square B is Q1 Q2 Q3 Q4 and the constructed triangle T is T1 T2 T3.
|Time Limit:||2 sec|
|Source Limit:||50000 Bytes|
|Languages:||C, CPP14, JAVA, PYTH, PYTH 3.6, PYPY, CS2, PAS fpc, PAS gpc, RUBY, PHP, GO, NODEJS, HASK, rust, SCALA, swift, D, PERL, FORT, WSPC, ADA, CAML, ICK, BF, ASM, CLPS, PRLG, ICON, SCM qobi, PIKE, ST, NICE, LUA, BASH, NEM, LISP sbcl, LISP clisp, SCM guile, JS, ERL, TCL, kotlin, PERL6, TEXT, SCM chicken, PYP3, CLOJ, COB, FS|
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