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
import math
t = int(input())
while t>0:
    t -= 1
    s = input()
    x = int(input())
    confuse = []
    ans = [-1]*len(s)
    flag = False
    for i in range(len(s)):
        if s[i] == '1':
            if i-x < 0:
                if i+x < len(s):
                    if ans[i+x] == 0:
                        print(-1)
                        flag = True
                        break
                else:
                    print(-1)
                    flag = True
                    break
                ans[i+x] = 1
            else:
                if ans[i-x] == 1:
                    continue
                elif ans[i-x] == 0:
                    if i+x >= len(s) or ans[i+x] == 0:
                        print(-1)
                        flag = True
                        break
                    else:
                        ans[i+x] = 1
                else:
                    if i+x < len(s):
                        if ans[i+x] == 1:
                            continue
                        elif ans[i+x] == 0:
                            ans[i-x] = 1
                            continue
                        else:
                            confuse.append((i-x, i+x)) 
                    else:
                        ans[i-x] = 1
        else:
            if i-x >= 0:
                if ans[i-x] == 1:
                    print(-1)
                    flag = True
                    break
                else:
                    ans[i-x] = 0
                    if i+x < len(s):
                        if ans[i+x] == 1:
                            print(-1)
                            flag = True
                            break
                        else:
                            ans[i+x] = 0
            else:
                if i+x < len(s):
                    if ans[i+x] == 1:
                        print(-1)
                        flag = True
                        continue
                    else:
                        ans[i+x] = 0
                else:
                    pass

    if not flag:
        for pair in confuse:
            if ans[pair[0]] == 0 and ans[pair[1]] == 0:
                print(-1)
                flag = True
                break
        if not flag:
            for i in range(len(s)):
                if ans[i] == -1:
                    ans[i] = 1
                ans[i] = str(ans[i])
            print(''.join(ans))




    



