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2-sat

brute force

constructive algorithms

greedy

*1500

No tag edit access

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C. Binary String Reconstruction

time limit per test

2 secondsmemory limit per test

256 megabytesinput

standard inputoutput

standard outputConsider the following process. You have a binary string (a string where each character is either 0 or 1) $$$w$$$ of length $$$n$$$ and an integer $$$x$$$. You build a new binary string $$$s$$$ consisting of $$$n$$$ characters. The $$$i$$$-th character of $$$s$$$ is chosen as follows:

- if the character $$$w_{i-x}$$$ exists and is equal to 1, then $$$s_i$$$ is 1 (formally, if $$$i > x$$$ and $$$w_{i-x} = $$$ 1, then $$$s_i = $$$ 1);
- if the character $$$w_{i+x}$$$ exists and is equal to 1, then $$$s_i$$$ is 1 (formally, if $$$i + x \le n$$$ and $$$w_{i+x} = $$$ 1, then $$$s_i = $$$ 1);
- if both of the aforementioned conditions are false, then $$$s_i$$$ is 0.

You are given the integer $$$x$$$ and the resulting string $$$s$$$. Reconstruct the original string $$$w$$$.

Input

The first line contains one integer $$$t$$$ ($$$1 \le t \le 1000$$$) — the number of test cases.

Each test case consists of two lines. The first line contains the resulting string $$$s$$$ ($$$2 \le |s| \le 10^5$$$, each character of $$$s$$$ is either 0 or 1). The second line contains one integer $$$x$$$ ($$$1 \le x \le |s| - 1$$$).

The total length of all strings $$$s$$$ in the input does not exceed $$$10^5$$$.

Output

For each test case, print the answer on a separate line as follows:

- if no string $$$w$$$ can produce the string $$$s$$$ at the end of the process, print $$$-1$$$;
- otherwise, print the binary string $$$w$$$ consisting of $$$|s|$$$ characters. If there are multiple answers, print any of them.

Example

Input

3 101110 2 01 1 110 1

Output

111011 10 -1

Codeforces (c) Copyright 2010-2023 Mike Mirzayanov

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