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
from sys import stdin, stdout, setrecursionlimit
from collections import deque, defaultdict, Counter
from heapq import heappush, heappop
from functools import lru_cache
import math

#setrecursionlimit(10**6)
rl = lambda: stdin.readline()
rll = lambda: stdin.readline().split()
rli = lambda: map(int, stdin.readline().split())
rlf = lambda: map(float, stdin.readline().split())

INF, NINF = float('inf'), float('-inf')
MOD = 10**9 + 7

def main():
	T = int(rl())
	for _ in range(T):
		s = [int(d) for d in list(rll()[0])]
		x = int(rl())
		n = len(s)
		w = [1 for _ in range(n)]
		for i, d in enumerate(s):
			if d == 0:
				if i - x >= 0:
					w[i-x] = 0
				if i + x < n: 
					w[i+x] = 0
		exists = True
		for i, d in enumerate(w):
			if s[i] == 0: continue
			flag = False
			L = w[i-x] if i-x >= 0 else None
			R = w[i+x] if i+x < n else None
			if i - x >= 0 and w[i-x] == 1:
				flag = True
			elif i + x < n and w[i+x] == 1:
				flag = True
			if not flag:
				exists = False
		if not exists:
			print(-1)
		else:
			print("".join(str(d) for d in w))
	stdout.close()

if __name__ == "__main__":
	main()