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
t = input()

for _ in xrange(t):
    s = raw_input().strip()
    x = input()
    n = len(s)
    w = {}

    for i, e in enumerate(s):
        i += 1
        if e == "0":
            if i > x:
                w[i - x] = "0"
            if i + x <= n :
                w[i + x] = "0"

    possible = True
    ans = ""
    for i in xrange(1, n + 1):
        if i - x >= 1 and w.get(i - x, "1") == "1":
            if s[i - 1] != "1":
                possible = False
                break
        if i + x <= n and w.get(i + x, "1") == "1":
            if s[i - 1] != "1":
                possible = False
                break
        ans += w.get(i, "1")
    
    if not possible:
        print -1
    else:
        pos = list(ans)

        for i in xrange(n):
            if i - x >= 0 and ans[i - x] == "1":
                pos[i] = "1"
            elif i + x <= n - 1 and ans[i + x] == "1":
                pos[i] = "1"
            else:
                pos[i] = "0"

                
        # print "".join(pos), s, ans
        if "".join(pos) == s:
            print ans
        else:
            print -1
