1400_C. Binary String Reconstruction
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
```python
def fn1(n,num,lis):
    for i in range(n):
        if i-x>=0 and num[i-x]==1:
            lis.append(1)
        elif i+x<n and num[i+x]==1:
            lis.append(1)
        else:
            lis.append(0)
def fn2(st,s,num):
    if st==s:
        for i in num:
            print(i,end="")
        print()
    else:
        print(-1)
for _ in range(int(input())):
    s=input()
    n=len(s)
    x=int(input())
    num=[1 for i in range(n)]
    f1=0
    for i in range(n):
        di=int(s[i])
        if i-x<0 and i+x>=n:
            if di==0:
                num[i]=0
        else:
            if i-x<0 and i+x<n:
                if di==0:
                    num[i+x]=0
            elif i-x>=0 and i+x>=n:
                if di==0:
                    num[i-x]=0
            elif i-x>=0 and i+x<n:
                if di==0:
                    num[i-x]=0
                    num[i+x]=0
    lis=[]
    fn1(n,num,lis)
    st=""
    for i in lis:
        st+=str(i)
    fn2(st,s,num)
```