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 controller(s, x):
    n = len(s)
    w = list('1'*n)
    a = -x
    b = x
    for si in s:
        if si == '0':
            if a >= 0:
                w[a] = '0'
            if b < n:
                w[b] = '0'
        elif a < 0 and b >= n:
            return -1
        # if a >= 0 and si == '0':
        #     w[a] = '0'
        # if b < n and si == '0':
        #     w[b] = '0'
        # if a < 0 and b >= n and si == '1':
        #     return '-1'
        a += 1
        b += 1
    a = -x
    b = x
    for si in s:
        """ s[i] w[a] w[b]
        1 1 1
        1 1 0
        1 0 1
        1 0 0   -- Conflict
        0 1 1   -- Conflict (but won't happen)
        0 1 0   -- Conflict (but won't happen)
        0 0 1   -- Conflict (but won't happen)
        0 0 0
        0 1 any -- Conflict (but won't happen)
        1 0 any -- Conflict
        """
        if si == '1':
            if a < 0:
                if b < n and w[b] == '0':
                    return '-1'
            elif w[a] == '0':
                if b < n:
                    if w[b] == '0':
                        return -1
                else:
                    return '-1'
            # elif w[a] == '0' and (b >= n or w[b] == '0'):
            #     return '-1'
            # else:
            #     if b < n:
            #         if w[a] == '0' == w[b]:
            #             return '-1'
            #     elif w[a] == '0':
            #         return '-1'
        a += 1
        b += 1
    return ''.join(w)

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

if __name__ == '__main__':
    c_in()

