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
#Problem C
#map(int,i().split())
import sys
def i():
    return sys.stdin.readline()[:-1]

def getOutList(n,x,binList):
    outList = [False]*n
    for b in range(n-x):
        outList[b] = binList[b+x]
    for b in range(x,n):
        outList[b] = outList[b] or binList[b-x]
    return outList

cases = int(i())
for a in range(cases):
    inStr = i()
    binList = list(x=='1' for x in inStr)
    x = int(i())
    n = len(binList)
    posIn = [True]*n
    for b in range(n-x):
        if not binList[b]:
            posIn[b+x] = False
    for b in range(x,n):
        if not binList[b]:
            posIn[b-x] = False

    if not getOutList(n,x,posIn) == binList:
        print(-1)
    else:
        outStr = ""
        for bit in posIn:
            outStr += "1" if bit else "0"
        print(outStr)
