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
for _ in range(int(input())):
    s = input()

    x = int(input())
    s1 = [-1 for i in range(len(s))]
    n = len(s)
    flag = 0
    for i in range(len(s)):
        if s[i] == '0':
            if i-x>=0 and i+x<=n-1:
                if (s1[i-x]==0 or s1[i-x]==-1):
                    s1[i-x]=0
                else:
                    flag=1
                    break
                if (s1[i+x]==0 or s1[i+x]==-1):
                    s1[i+x]=0

                else:
                    flag=1
                    break
                continue

            if i - x < 0 and i + x > n - 1:
                if s1[i] == -1 or s1[i] == 0:
                    s1[i] = 0

                else:
                    ##print(i)
                    flag = 1
                    break
                continue
            if i - x < 0:
                if s1[i + x] == -1 or s1[i + x] == 0:
                    s1[i + x] = 0



                else:
                    ## print(i)
                    flag = 1
                    break
                continue
            else:
                if s1[i - x] == -1 or s1[i - x] == 0:
                    s1[i - x] = 0

                else:
                    ##print(i)
                    flag = 1
                    break
            ##print(s1)
        if s[i] == '1':
            if i - x < 0 and i + x > n - 1:
                flag = 1
                break
            if i-x>=0 and i+x<=n-1:

                if s1[i-x]==0:
                    s1[i+x]=1
                else:
                    s1[i-x]=1
                continue

            if i - x < 0:
                if s1[i + x] == -1 or s1[i + x] == 1:
                    s1[i + x] = 1
                else:
                    ##print(i)
                    flag = 1
                    break
                continue
            if i + x > n - 1:
                ##print(s1)
                if s1[i - x] == -1 or s1[i - x] == 1:
                    s1[i - x] = 1
                else:
                    ##print(i)
                    flag = 1
                    break

           ## print(s1)
    if flag == 1:
        print(-1)
        continue

    for i in range(len(s1)):
        if s1[i] == -1:
            s1[i] = 1
    s3 = ""
    for i in range(len(s1)):
        s3 += str(s1[i])
    print(s3)
