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 i in range(0,t):
    str1=input()
    m=int(input())
    l1=[]
    y=len(str1)
    for i in range(0,y):
        l1.append(1)
    for i in range(0,y):
        if(str1[i]=='0'):
            if((i-m)>=0):
                l1[i-m]=0
            if(i+m<y):
                l1[i+m]=0
    ct=0
    for i in range(0,y):
        if(str1[i]=='1'):
            if((i-m)<0 and(i+m)>=y):
                ct+=1
                break
            if((i-m)<0):
                if(l1[i+m]==0):
                    ct+=1
                    break
            if((i+m)>=y):
                if(l1[i-m]==0):
                    ct+=1
                    break
            if((i-m)>=0 and (i+m)<y):
                if(l1[i-m]==0 and l1[i+m]==0):
                    ct+=1
                    break
    if(ct==0):
        print(*l1,sep="")
    else:
        print("-1")
                
                
    