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
UNDEF = '?'

def forward(w, x):
    s =[ '?' ]* len(w)
    for i in range(len(w)):
        if i - x >= 0 and w[i - x] == '1':
            s[i] = '1'
        elif i + x < len(w) and w[i + x] == '1':
            s[i] = '1'
        else:
            s[i] = '0'
    return (''.join(s))


def solve(s, x):
    n = len(s)
    w = [UNDEF] * n
    for j in range(x):
        if j + x < n:
            w[j + x] = s[j]
        i = n - j - 1
        if i - x >= 0:
            if w[i - x] != UNDEF and w[i - x] != s[i]:
                return UNDEF
            w[i - x] = s[i]

    for i in range(x, n - x):
        '''
        if s[i] == '1':
            if '1' in (w[i - x], w[i + x]):
                continue
            if w[i - x] == UNDEF:
                w[i - x] = '1'
                continue
            if w[i + x] == UNDEF:
                w[i + x] = '1'
            return UNDEF
        elif s[i] == '0':
            if '1' in (w[i - x], w[i + x]):
                return UNDEF
            w[i - x] = '0'
            w[i + x] = '0'
        '''
        if s[i] == '0':
            if '1' in (w[i - x], w[i + x]):
                return UNDEF
            w[i - x] = '0'
            w[i + x] = '0'

    w = ''.join(w).replace('?', '1')
    return (w if forward(w, x) == s else UNDEF)


for _ in range(int(input())):
    s = input()
    x = int(input())
    ans = solve(s, x)
    if ans == UNDEF:
        print(-1)
    else:
        print(ans)

