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
import math
import collections
import bisect
import itertools
import decimal

# import numpy as np

sys.setrecursionlimit(10 ** 7)
INF = 10 ** 20
MOD = 10 ** 9 + 7
# MOD = 998244353

ni = lambda: int(sys.stdin.readline().rstrip())
ns = lambda: map(int, sys.stdin.readline().rstrip().split())
na = lambda: list(map(int, sys.stdin.readline().rstrip().split()))
na1 = lambda: list(map(lambda x: int(x) - 1, sys.stdin.readline().rstrip().split()))


# ===CODE===

def main():
    t = ni()
    for _ in range(t):
        s = input()
        x = ni()

        ans = [1 for _ in range(len(s))]
        for i, si in enumerate(s):
            if si == "0":
                if i - x >= 0:
                    ans[i - x] = 0
                if i + x < len(s):
                    ans[i + x] = 0

        flg = True
        for i, si in enumerate(s):
            if si == "1":
                flg1, flg2 = False, False
                if i - x >= 0:
                    flg1 = ans[i - x]
                if i + x < len(s):
                    flg2 = ans[i + x]
                if not (flg1 or flg2):
                    flg = False
                    break

        if flg:
            print(*ans, sep="")
        else:
            print(-1)


if __name__ == '__main__':
    main()
