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
#   ==========     //\\       //||     ||====//||
#       ||        //  \\        ||     ||   // ||
#       ||       //====\\       ||     ||  //  ||
#       ||      //      \\      ||     || //   ||
#   ========== //        \\  ========  ||//====|| 
#  code

def main():
    t = int(input())
    for _ in range(t):
        s = input()
        x = int(input())
        n = len(s)

        w = ['1'] * n

        for i in range(n):
            if i + x < n:
                if s[i + x] == '0':
                    w[i] = '0'
            if i - x >= 0:
                if s[i - x] == '0':
                    w[i] = '0'
        
        ok = True
        for i in range(n):
            if s[i] == '0':
                if i + x < n:
                    if w[i + x] == '1':
                        ok = False
                        break
                if i - x >= 0:
                    if w[i - x] == '1':
                        ok = False
                        break
            else:
                if i + x < n and i - x >= 0:
                    if w[i + x] == '0' and w[i - x] == '0':
                        ok = False
                        break
                if i + x >= n and i - x >= 0:
                    if w[i - x] == '0':
                        ok = False
                        break
                if i + x < n and i - x < 0:
                    if w[i + x] == '0':
                        ok = False
                        break
                if i + x >= n and i - x < 0:
                    ok = False
                    break

        print(''.join(w) if ok else -1)
    return

if __name__ == "__main__":
    main()