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,os,io
from collections import defaultdict
# input = io.BytesIO(os.read(0, os.fstat(0).st_size)).readline

for _ in range (int(input())):
    n,x = [int(i) for i in input().split()]
    dic = defaultdict(lambda: 0)
    s = input()
    cnt = 0
    zero = 0
    mini = 10**10
    maxi = -10**10
    for i in s:
        if i=='0':
            cnt+=1
        else:
            cnt-=1
        dic[cnt]+=1
        if cnt==0:
            zero+=1
        mini = min(mini,cnt)
        maxi = max(maxi,cnt)
    last = 0
    if cnt==0:
        if x in dic:
            print(-1)
        else:
            print(0)
    elif cnt>0:
        ans = 0
        mm = (x-maxi)//cnt
        if mm>0:
            mm-=1
            last = mm*cnt
        while(last+mini)<=x:
            if (x-last) in dic:
                ans+=dic[x-last]
            last+=cnt
        if x==0:
            ans+=1
        print(ans)
    else:
        ans = 0
        mm = (abs(x)-abs(mini))//abs(cnt)
        if mm>1:
            mm = abs(mm)-2
            last = mm*cnt
        while(last + maxi) >= x:
            if (x-last) in dic:
                ans+=dic[x-last]
            last += cnt
        if x==0:
            ans+=1
        print(ans)