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
from collections import defaultdict

t = int(input())
for _ in range(t):
    s = input()
    x = int(input())
    before = 0 - x
    after = 0 + x
    n = len(s)
    w = [-1] * n
    Dict = defaultdict(int)
    flag = 0
    #print(len(s))
    for i in range(len(s)):
        #print(i)
        if s[i] == "1":
            if before >= 0 and (Dict[before] == 0 or w[before] == 1):
                w[before] = 1
                Dict[before] += 1
            elif after < n and (Dict[after] == 0 or w[after] == 1):
                w[after] = 1
                Dict[after] += 1
            else:
                flag = 1
                break
        else:
            if before < 0:
                temp_b = 1
            else:
                temp_b = 0
            if after >= n:
                temp_a = 1
            else:
                temp_a = 0
            if before >= 0 and (Dict[before] == 0 or w[before] == 0):
                w[before] = 0
                Dict[before] += 1
                temp_b = 1
            if after < n and (Dict[after] == 0 or w[after] == 0):
                w[after] = 0
                Dict[after] += 1
                temp_a = 1
            if temp_b == 0 or temp_a == 0:
                flag = 1
                break
        before += 1
        after += 1
    if flag == 1:
        print(-1)
    else:
        for i in range(n):
            if w[i] == -1:
                w[i] = 1
        w = [str(i) for i in w]
        print("".join(w))
    ## 1 1 0
    ## 0 1 0
    ## 0 1 1  1 1 0
    ## 1 2 3 4 5
    ## 1 -> 3     ## 1-> 2
    ## 2 -> 4     ## 2 -> 1, 3
    ## 3 -> 1,5   ## 3->2,4
    ## 4 -> 2     ## 4-> 3,4
    ## 5 -> 3     ## 5->4
