Problem: You are given string s of length n consisting of 0-s and 1-s. You build an infinite string t as a concatenation of an infinite number of strings s, or t = ssss ... For example, if s = 10010, then t = 100101001010010...

Calculate the number of prefixes of t with balance equal to x. The balance of some string q is equal to cnt_{0, q} - cnt_{1, q}, where cnt_{0, q} is the number of occurrences of 0 in q, and cnt_{1, q} is the number of occurrences of 1 in q. The number of such prefixes can be infinite; if it is so, you must say that.

A prefix is a string consisting of several first letters of a given string, without any reorders. An empty prefix is also a valid prefix. For example, the string "abcd" has 5 prefixes: empty string, "a", "ab", "abc" and "abcd".

Input

The first line contains the single integer T (1 ≤ T ≤ 100) — the number of test cases.

Next 2T lines contain descriptions of test cases — two lines per test case. The first line contains two integers n and x (1 ≤ n ≤ 10^5, -10^9 ≤ x ≤ 10^9) — the length of string s and the desired balance, respectively.

The second line contains the binary string s (|s| = n, s_i ∈ \{0, 1\}).

It's guaranteed that the total sum of n doesn't exceed 10^5.

Output

Print T integers — one per test case. For each test case print the number of prefixes or -1 if there is an infinite number of such prefixes.

Example

Input


4
6 10
010010
5 3
10101
1 0
0
2 0
01


Output


3
0
1
-1

Note

In the first test case, there are 3 good prefixes of t: with length 28, 30 and 32.

Solution (in PYTHON3):

Solution:
from sys import stdin

#n=int(stdin.readline().strip())
#n,m=map(int,stdin.readline().strip())
#s=list(map(int,stdin.readline().strip()))

t=int(stdin.readline().strip())
for tt in range(t):
  n,m=map(int,stdin.readline().strip().split())
  s=stdin.readline().strip()
  bal=0
  men=0
  may=0
  cnt=0
  arr=[0 for i in range(n+10)]
  arr1=[0 for i in range(n+10)]
  for i in range(n):
    if s[i]=='0':
      bal+=1
    else:
      bal-=1
    if bal>=0:
      arr[bal]+=1
    else:
      arr1[-bal]+=1
    if bal==m:
      cnt+=1
  ans=0

  if cnt>0 and bal==0:
    print(-1)
    continue
  if cnt==0 and bal==0:
    print(0)
    continue
  for i in range(n+10):
    dif=m-i
    if (dif%bal)==0 and bal*dif>=0:
        ans+=arr[i]
  for i in range(1,n+10):
    dif=m+i
    if (dif%bal)==0 and bal*dif>=0:
        ans+=arr1[i]
  if m==0:
    ans+=1
  print(ans)