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
input = sys.stdin.readline
INF = 10

def solution():
    s = list(map(int, input().rstrip()))
    x = int(input())

    N = len(s)

    ans = [-1] * N
    flag = True
    for i in range(N):
        if i - x < 0: L = INF
        else: L = ans[i - x]
        if i + x >= N: R = INF
        else: R = ans[i + x]

        if s[i] == 1:
            if L == 1 or R == 1:
                continue
            elif L == -1:
                ans[i - x] = 1
            elif R == -1:
                ans[i + x] = 1
            else:
                flag = False

        if s[i] == 0:
            if L == 0 and R == 0:
                continue
            elif L != 1 and R != 1:
                if L == -1: ans[i - x] = 0
                if R == -1: ans[i + x] = 0
            else:
                flag = False
    if not flag:
        print(-1)
    else:
        for i in range(N):
            if ans[i] == -1:
                ans[i] = 1
        print(''.join(map(str, ans)))

if __name__ == "__main__":
     T = int(input())
     for _ in range(T):
         solution()