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
class Conflict(Exception): pass

# w[i] = 1 if (w[i-x] exists equal to 1 or w[i+x] exists equal to 1) else 0
def controller(s, x):
    n = len(s)
    s = [int(i) for i in s]
    w = [-1]*n
    constraints = []
    def set(idx, val):
        if w[idx] != val:
            if w[idx] != -1:
                # print(f"Conflict set {idx} {val}")
                raise Conflict()
            w[idx] = val
    try:
        for i in range(n):
            a, b = i-x, i+x
            has_a, has_b = a>=0, b<n
            if has_a and has_b:
                if s[i] == 0:
                    set(a,0)
                    set(b,0)
                else:
                    constraints.append(i)
            elif has_a:
                set(a, s[i])
            elif has_b:
                set(b, s[i])
            elif s[i] != 0:
                # print("Conflict any any 1")
                raise Conflict()
        for i in constraints:
            if w[i-x] < 0:
                w[i-x] = 1
            elif w[i+x] < 0:
                w[i+x] = 1
            elif w[i-x] + w[i+x] == 0:
                # print("Conflict constraints")
                raise Conflict()
    except Conflict:
        return -1
    return ''.join('1' if i<0 else str(i) for i in w)

def c_in():
    import sys, os
    # try:
    #     file = open(os.path.join(sys.argv[0], r'../in-c-2.txt'))
    # except:
    file = sys.stdin
    n_test_case = int(file.readline())
    for i in range(n_test_case):
        w = file.readline().rstrip()
        x = int(file.readline())
        print(controller(w,x))

if __name__ == '__main__':
    c_in()

