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 > 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 ≤ 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 ≤ t ≤ 1000) — the number of test cases.

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

inputFormat

Input

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

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

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

outputFormat

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

样例

3
101110
2
01
1
110
1

111011
10
-1

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