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
t=int(input())
for g in range(0,t):
    s=list(input())
    a=[]
    for i in range(0,len(s)):
        a.append(-1)
    x=int(input())
    ans=1
    for i in range(0,len(s)):
        if(s[i]=="0"):
            if(i+x<len(s)):
                a[i+x]="0"
            if(i-x>=0):
                a[i-x]="0"
        else:
            done=0
            if(i-x>=0):
                if(a[i-x]==-1 or a[i-x]=="1"):
                    done=1
                    a[i-x]="1"
            if(i+x<len(s) and done==0):
                if(a[i+x]==-1):
                    done=1
                    a[i+x]="1"
            if(done==0):
                ans=0
                break
    if(ans==0):
        print(-1)
    else:
        ans=1
        for i in range(len(s)):
            if(s[i]=="0"):
                done=1
                if(i+x<len(s) and a[i+x]!="0"):
                    done=0
                if(i-x>=0 and a[i-x]!="0"):
                    done=0
                if(done==0):
                    ans=0
                    break
            else:
                done=0
                if(i+x<len(s) and a[i+x]=="1"):
                    done=1
                if(i-x>=0 and a[i-x]=="1"):
                    done=1
                if(done==0):
                    ans=0
                    break
        final=""
        if(ans==0):
            print(-1)
        else:
            for i in range(0,len(s)):
                if(a[i]==-1):
                    a[i]="1"
                final+=(a[i])
            print(final)


    
    

                

    