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 io
import os

from collections import Counter, defaultdict, deque


def WToS(W, X):
    N = len(W)
    S = [0 for i in range(N)]
    for i in range(N):

        S[i] = "0"
        if i - X >= 0 and W[i - X] == "1":
            S[i] = "1"

        if i + X < N and W[i + X] == "1":
            S[i] = "1"

    return "".join(map(str, S))


def solve(S, X):
    N = len(S)
    W = ['1' for i in range(N)]
    for i, x in enumerate(S):
        if x == "0":
            if i + X < N:
                W[i + X] = "0"
            if i - X >= 0:
                W[i - X] = "0"

    W = "".join(map(str, W))
    if WToS(W, X) == S:
        return W
    return -1


if __name__ == "__main__":
    input = io.BytesIO(os.read(0, os.fstat(0).st_size)).readline

    TC = int(input())
    for tc in range(1, TC + 1):
        S = input().decode().rstrip()
        (X,) = [int(x) for x in input().split()]
        ans = solve(S, X)
        print(ans)
