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 sys
reader = (s.rstrip() for s in sys.stdin)
input = reader.__next__

def gift():
    for _ in range(t):
        string = input()
        x = int(input())
        n = len(string)

        markpoint=[]
        Failed=False
        for i in range(n):
            if string[i] == '0':
                markpoint.append(i)

        dic={}
        for ele in markpoint:
            if ele-x>=0:
                dic[ele-x]=True
            if ele+x<=n-1:
                dic[ele+x]=True
        #print(dic)
        for ele in dic:
            if ele-x>=0:
                if ele-2*x>=0:
                    if dic.get(ele-2*x,False):
                        if string[ele-x]!='0':
                            Failed=True
                            break
                    else:
                         if string[ele-x]!='1':
                            Failed=True
                            break                       
                else:
                    if string[ele-x]!='0':
                        Failed=True
                        break
            
            if ele+x<=n-1:
                if ele+2*x<=n-1:
                    if dic.get(ele+2*x,False):
                        if string[ele+x]!='0':
                            Failed=True
                            break
                    else:
                         if string[ele+x]!='1':
                            Failed=True
                            break 
                else:
                    if string[ele+x]!='0':
                        Failed=True
                        break
        if Failed:
            yield -1
        else:
            ans = []
            for i in range(n):
                if dic.get(i,False):
                    ans.append('0')
                else:
                    ans.append('1')
            kap=''.join(ans)
            right=True
            for i in range(n):
                curr=False
                if i-x>=0:
                    if kap[i-x]=='1':
                        curr=True
                if i+x<=n-1:
                    if kap[i+x]=='1':
                        curr=True
                if curr:
                    if string[i]!='1':
                        right=False
                        break
                else:
                    if string[i]!='0':
                        right=False
                        break
            if right:
                yield kap
            else:
                yield -1
if __name__ == '__main__':
    t= int(input())
    ans = gift()
    print(*ans,sep='\n')
            


#"{} {} {}".format(maxele,minele,minele)





#3 2 3 3


#1100
    
#1000
#    
