Chef and Subset Additions Solution|Codesheff

Chef is asked to write a program that takes an array A$A$ of length N$N$ and two integers X,Y$X,Y$ as input and modifies it as follows:

• Choose a random subset of elements of A$A$ (possibly empty)
• Increase all the elements of the chosen subset by X$X$
• Increase the remaining elements in A$A$ by Y$Y$

You are given N$N$, X$X$, Y$Y$, A$A$ and the array B$B$ that is returned by Chef's program. Determine whether Chef's program gave the correct output.

Input Format

• The first line contains an integer T$T$, the number of testcases. The description of the T$T$ testcases follow.
• Each testcase contains 3$3$ lines.
• The first line of each testcase contains a three space separated integers N,X,Y$N,X,Y$ respectively.
• The second line of each testcase contains N$N$ space separate integers, the elements of the array A$A$.
• The third line of each testcase contains N$N$ space separate integers, the elements of the array B$B$.

Output Format

• For each testcase, print in a single line either yes or no, according to whether Chef's program gave a valid output or not.
• You may output the answers in any case, for example the words Yes, YeS, YES, yES are all considered equivalent to yes.

Constraints

• 1≤T≤10$1\le T\le 10$
• 1≤N≤1000$1\le N\le 1000$
• 0≤X,Y≤1000$0\le X,Y\le 1000$
• 0≤Ai≤Bi≤1000$0\le A_i\le B_i\le 1000$ for all indices i$i$

Subtasks

Subtask #1 (100 points): original constraints

Sample Input 1 

3
3 2 5
9 5 1
11 10 3
3 2 5
9 5 1
11 7 3
3 2 5
9 5 1
11 7 7

Sample Output 1 

Yes
Yes
No

Explanation

Test Case 1: The array A$A$ is {9,5,1}$\{9,5,1\}$. If the chosen elements are 9,1$9,1$ then the expected output would be {11,10,3}$\{11,10,3\}$, so the answer is yes.

Test Case 2: The array A$A$ is {9,5,1}$\{9,5,1\}$. If the chosen elements are 9,5,1$9,5,1$ then the expected output would be {11,7,3}$\{11,7,3\}$, so the answer is yes.

Test Case 3: The array A$A$ is {9,5,1}$\{9,5,1\}$. There is no subset that can be chosen so that the expected output would be {11,7,7}$\{11,7,7\}$, so Chef's implementation must be incorrect and the answer is no.

Solution:

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