Jackpot queries

Problem Description

You are visiting a fair in byteland. You are shopping and want to buy Q items. Each item cost exactly B[i] amount of money.

You have no money but you have a magical bag on which you can apply an operation any times you want.

In bag there are N integers denoted by array A.

In one operation, You choose two integer X Y from A and deposit all of the amount of money M you have, this will magically increase your money by X ⊕ Y.

Note: You have to deposit all money you have otherwise you will be exiled from Byteland for your greed. Also, shopkeepers have no change, So you have to pay exact amount. :p

Treating each item as independent and starting with 0 amount of money, Can you find if we can buy each item?

Problem Constraints

2 ≤ N ≤ 1000
1 ≤ A[i] ≤ 10000
1 ≤ Q ≤ 100000
0 ≤ B[i] ≤ 10⁹

Input Format

First argument contains an integer array A of size N. Second argument contains an integer array B of size Q.

Output Format

Return a binary string of size Q containing i^th as 1 if its possible to buy i^th item else 0.

Example Input

Input 1:

A = [1, 2], B = [3, 5, 10, 15]

Input 2:

A = [1, 2, 3], B = [1, 5, 10]

Example Output

Output 1:

"1001"

Output 2:

"111"

Example Explanation

Explanation 1:


    Note if same number are choosen then xor is 0 so only way to increase is by 3 (1 xor 2). So, all multiple of 3 can be paid off.

NOTE: You only need to implement the given function. Do not read input, instead use the arguments to the function. Do not print the output, instead return values as specified. Still have a question? Checkout Sample Codes for more details.

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