Educational Codeforces Round 81 B. Infinite Prefixes
B. Infinite Prefixes
time limit per test
2 seconds
memory limit per test
256 megabytes
input
standard input
output
standard output
You are given string ss of length nn consisting of 0-s and 1-s. You build an infinite string tt as a concatenation of an infinite number of strings ss, or t=ssss…t=ssss… For example, if s=s= 10010, then t=t= 100101001010010...
Calculate the number of prefixes of tt with balance equal to xx. The balance of some string qq is equal to cnt0,q−cnt1,qcnt0,q−cnt1,q, where cnt0,qcnt0,q is the number of occurrences of 0 in qq, and cnt1,qcnt1,q is the number of occurrences of 1 in qq. 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 TT (1≤T≤1001≤T≤100) — the number of test cases.
Next 2T2T lines contain descriptions of test cases — two lines per test case. The first line contains two integers nn and xx (1≤n≤1051≤n≤105, −109≤x≤109−109≤x≤109) — the length of string ss and the desired balance, respectively.
The second line contains the binary string ss (|s|=n|s|=n, si∈{0,1}si∈{0,1}).
It's guaranteed that the total sum of nn doesn't exceed 105105.
Output
Print TT integers — one per test case. For each test case print the number of prefixes or −1−1 if there is an infinite number of such prefixes.
Example
input
Copy
4
6 10
010010
5 3
10101
1 0
0
2 0
01
output
Copy
3
0
1
-1
Note
In the first test case, there are 3 good prefixes of tt: with length 2828, 3030 and 3232.
题目链接:https://codeforces.com/contest/1295/problem/B
题意:
给定一个只含有'0','1' 的字符串,定义一个字符串的q值为'0'字符的个数减去'1'字符的个数
问给定字符串s的所有前缀中(包括空字符串)q值为x的个数。
思路:
分类讨论:
当s的q值为0的时候:
如果s的所有前缀中有出现q值为x的时候,答案是-1
否则为0
当s的q值不为0的时候:
维护出一个周期的q值增量all。
一个周期中到第i个字符的前缀q值为cnt,
当满足$(x - cnt) mod all == 0 $ 且 $ (x - cnt) / all >= 0 $ 答案就加一
可以理解为某个位置的前缀和加上n个周期的贡献为x且贡献次数即之前的周期次数大于等于0次
代码
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