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
def split(ini): 
    return [c for c in ini]

i = int(input())
for _ in range(i):
    inlist = [int(j) for j in split(input())]
    outlist = [2 for _ in range(len(inlist))]
    x = int(input())
    totbreak = True
    for k in range(len(inlist)):
        bino = inlist[k]
        if bino == 0:
            if k - x >= 0:
                if outlist[k - x] == 2:
                    outlist[k - x] = 0
                if outlist[k - x] == 1:
                    print(-1)
                    totbreak = False
                    break
            if k + x < len(inlist):
                if outlist[k + x] == 2:
                    outlist[k + x] = 0
                if outlist[k + x] == 1:
                    print(-1)
                    break
        else:
            breakbool = False
            if k - x >= 0:
                if outlist[k - x] == 2 or outlist[k - x] == 1:
                    outlist[k - x] = 1
                    breakbool = True
            if k + x < len(inlist) and not breakbool:
                outlist[k + x] = 1
                breakbool = True
            if not breakbool:
                print(-1)
                totbreak = False
                break
    if totbreak:
        for out in outlist:
            if out == 2:
                print(0, end="")
            else:
                print(out, end="")
        print()
                
                
            
        
    
