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 dfs(s1,s,x,index,visited):
    orig = index
    while index < len(s):
        visited.add(index)
        if s[index] == '0':
            if index-x >= 0:
                s1[index-x] = '0'

            if index+x < len(s):
                s1[index+x] = '0'

        index += 1

    index = orig
    #print(index)
    while index < len(s):
        if s[index] == '1':
            if index-x >= 0:
                if s1[index-x] == -1:
                    s1[index-x] = '1'

            if index+x < len(s):
                if s1[index+x] == -1:
                    s1[index+x] = '1'

        index += 1

def good(s1,s,x):
    for i in range(len(s)):
        if s[i] == '0':
            if i+x < len(s) and s1[i+x] != '0':
                return False
            if i-x >= 0 and s1[i-x] != '0':
                return False
        else:
            if ((i+x < len(s) and s1[i+x] != '1') or i+x >= len(s)) and ((i-x >= 0 and s1[i-x] != '1') or i-x < 0):
                return False

    return True

def solve(s,x,ans):
    s1 = [-1]*len(s)
    visited = set()
    for i in range(len(s)):
        if i not in visited:
            dfs(s1,s,x,i,visited)

    for i in range(len(s)):
        if s1[i] == -1:
            s1[i] = '1'
            
    if good(s1,s,x):
        ans.append(s1)
    else:
        ans.append(['-1'])

def main():
    t = int(input())
    ans = []
    for i in range(t):
        s = input()
        x = int(input())
        solve(s,x,ans)

    for i in ans:
        print(''.join(i))


main()
