CF1400C.Binary String Reconstruction

Consider 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 $i \gt x$ 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 $w$.

考虑如下过程：你有一个长度为 $n$ 的二进制字符串（即每个字符均为 0 或 1 的字符串）$w$ 和一个整数 $x$。你将构建一个新的二进制字符串 $s$，其长度也为 $n$。$s$ 的第 $i$ 个字符按如下规则确定：

• 若字符 $w_{i-x}$ 存在且等于 1，则 $s_i = 1$（形式化地，若 $i > x$ 且 $w_{i-x} = 1$，则 $s_i = 1$）；
• 若字符 $w_{i+x}$ 存在且等于 1，则 $s_i = 1$（形式化地，若 $i + x \le n$ 且 $w_{i+x} = 1$，则 $s_i = 1$）；
• 若上述两个条件均不满足，则 $s_i = 0$。

现给你整数 $x$ 和结果字符串 $s$，请重构原始字符串 $w$。

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 $10^5$.

第一行包含一个整数 $t$（$1 \le t \le 1000$）—— 测试用例的数量。

每个测试用例由两行组成。第一行包含结果字符串 $s$（$2 \le |s| \le 10^5$，$s$ 的每个字符均为 0 或 1）。第二行包含一个整数 $x$（$1 \le x \le |s| - 1$）。

输入中所有字符串 $s$ 的总长度不超过 $10^5$。

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.

对于每个测试用例，在单独一行中输出答案，规则如下：

• 如果不存在字符串 $w$ 能在该过程结束时生成字符串 $s$，则输出 $-1$；
• 否则，输出由 $|s|$ 个字符组成的二进制字符串 $w$。若存在多个合法答案，输出任意一个即可。