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:
import sys
from collections import Counter
 
# inf = open('input.txt', 'r')
# reader = (line.rstrip() for line in inf)
reader = (line.rstrip() for line in sys.stdin)
input = reader.__next__
 
def countPrefix(s, x):
    if x < 0:
        s = s.replace('0', '#').replace('1', '0').replace('#', '1')
        x = -x
    
    bal = 0
    ctr = Counter()
    maxBal = minBal = 0
    for c in s:
        if c == '0':
            bal += 1
        else:
            bal -= 1
        ctr[bal] += 1
        maxBal = max(maxBal, bal)
        minBal = min(minBal, bal)
        
#     print(s, bal)
#     print(x, maxBal)
    if bal == 0:
        if x <= maxBal:
            return -1
        else:
            return 0
    elif bal < 0:
        ans = 0
        if maxBal >= x:
            k = 0
            while maxBal + k * bal >= x:
                ans += ctr[x - k * bal]
                k += 1
    else:
        if maxBal >= x:
            k = 0
        else:
            k = (x - maxBal) // bal
        ans = 0
        while minBal + k * bal <= x:
            ans += ctr[x - k * bal]
            k += 1
    
    if x == 0:
        ans += 1
    return ans
 
t = int(input())
for _ in range(t):
    n, x = map(int, input().split())
    s = input()
    print(countPrefix(s, x))
 
# inf.close()