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
#!/usr/bin/env python3
import sys
input = sys.stdin.readline

t = int(input())
for _ in range(t):
    s = [int(item) for item in input().rstrip()]
    x = int(input())
    n = len(s)
    ret1 = [-1] * n
    for i in range(x, n):
        if not s[i]:
            ret1[i - x] = 0
    for i in range(n - x):
        if not s[i]:
            ret1[i + x] = 0
    for i in range(n):
        if ret1[i] == -1:
            ret1[i] = 1
    ret2 = [-1] * n
    for i in range(n):
        if i - x < 0:
            l = 0
        else:
            l = ret1[i-x]
        if i + x > n - 1:
            r = 0
        else:
            r = ret1[i+x]
        ret2[i] = l or r
    if ret2 != s:
        print(-1)
    else:
        print("".join([str(item) for item in ret1]))