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 math import *
import sys
input=sys.stdin.readline
t=int(input())
while t>0:
    t-=1
    n,x=map(int,input().split())
    a=list(input().rstrip())
    cnt=[0 for i in range(n+1)]
    for i in range(1,n+1):
        if a[i-1]=='0':
            cnt[i]=cnt[i-1]+1
        else:
            cnt[i]=cnt[i-1]-1
    #print(cnt[1:])        
    if cnt[n]==0 and x==0:
        print(-1)
        continue
    c=int(x==0)
    flag=0
    for i in range(1,n+1):
        if (x-cnt[i])==0:
            if cnt[n]==0:
                flag=1
                break
            c+=1
            #print(i,1)
    if flag:
        print(-1)
        continue
    for i in range(1,n+1):
        if cnt[n]==0:
            break
        #print("WTF",(x-cnt[i])%cnt[n]==0 , (x-cnt[i])//cnt[n]>1 , x/cnt[n]>0)
        if (x-cnt[i])%cnt[n]==0 and ( (x-cnt[i])//cnt[n]>0) :
            c+=1
            #print(i,cnt[i])
    print(c)