Problem:
Score : 600 points

Problem Statement

Given are two strings s and t consisting of lowercase English letters. Determine if the number of non-negative integers i satisfying the following condition is finite, and find the maximum value of such i if the number is finite.

There exists a non-negative integer j such that the concatenation of i copies of t is a substring of the concatenation of j copies of s.

Notes

A string a is a substring of another string b if and only if there exists an integer x (0 \leq x \leq |b| - |a|) such that, for any y (1 \leq y \leq |a|), a_y = b_{x+y} holds.

We assume that the concatenation of zero copies of any string is the empty string. From the definition above, the empty string is a substring of any string. Thus, for any two strings s and t, i = 0 satisfies the condition in the problem statement.

Constraints

1 \leq |s| \leq 5 \times 10^5

1 \leq |t| \leq 5 \times 10^5

s and t consist of lowercase English letters.

Input

Input is given from Standard Input in the following format:

s
t

Output

If the number of non-negative integers i satisfying the following condition is finite, print the maximum value of such i; if the number is infinite, print -1.

Sample Input 1

abcabab
ab

Sample Output 1

3

The concatenation of three copies of t, ababab, is a substring of the concatenation of two copies of s, abcabababcabab, so i = 3 satisfies the condition.

On the other hand, the concatenation of four copies of t, abababab, is not a substring of the concatenation of any number of copies of s, so i = 4 does not satisfy the condition.

Similarly, any integer greater than 4 does not satisfy the condition, either. Thus, the number of non-negative integers i satisfying the condition is finite, and the maximum value of such i is 3.

Sample Input 2

aa
aaaaaaa

Sample Output 2

-1

For any non-negative integer i, the concatenation of i copies of t is a substring of the concatenation of 4i copies of s. Thus, there are infinitely many non-negative integers i that satisfy the condition.

Sample Input 3

aba
baaab

Sample Output 3

0

As stated in Notes, i = 0 always satisfies the condition.

Solution in Rust (1.15.1) (judge verdict: Accepted)

macro_rules ! input { ( source = $ s : expr , $ ( $ r : tt ) * ) => { let mut iter = $ s . split_whitespace ( ) ; input_inner ! { iter , $ ( $ r ) * } } ; ( iter = $ iter : ident , $ ( $ r : tt ) * ) => { let s = { use std :: io :: Read ; let mut s = String :: new ( ) ; std :: io :: stdin ( ) . read_to_string ( & mut s ) . unwrap ( ) ; s } ; let mut $ iter = s . split_whitespace ( ) ; input_inner ! { $ iter , $ ( $ r ) * } } ; ( $ ( $ r : tt ) * ) => { let s = { use std :: io :: Read ; let mut s = String :: new ( ) ; std :: io :: stdin ( ) . read_to_string ( & mut s ) . unwrap ( ) ; s } ; let mut iter = s . split_whitespace ( ) ; input_inner ! { iter , $ ( $ r ) * } } ; }
macro_rules ! input_inner { ( $ iter : expr ) => { } ; ( $ iter : expr , ) => { } ; ( $ iter : expr , mut $ var : ident : $ t : tt $ ( $ r : tt ) * ) => { let mut $ var = read_value ! ( $ iter , $ t ) ; input_inner ! { $ iter $ ( $ r ) * } } ; ( $ iter : expr , mut $ var : ident $ ( $ r : tt ) * ) => { input_inner ! { $ iter , mut $ var : usize $ ( $ r ) * } } ; ( $ iter : expr , $ var : ident : $ t : tt $ ( $ r : tt ) * ) => { let $ var = read_value ! ( $ iter , $ t ) ; input_inner ! { $ iter $ ( $ r ) * } } ; ( $ iter : expr , $ var : ident $ ( $ r : tt ) * ) => { input_inner ! { $ iter , $ var : usize $ ( $ r ) * } } ; }
macro_rules ! read_value { ( $ iter : expr , ( $ ( $ t : tt ) ,* ) ) => { ( $ ( read_value ! ( $ iter , $ t ) ) ,* ) } ; ( $ iter : expr , [ $ t : tt ; $ len : expr ] ) => { ( 0 ..$ len ) . map ( | _ | read_value ! ( $ iter , $ t ) ) . collect ::< Vec < _ >> ( ) } ; ( $ iter : expr , { chars : $ base : expr } ) => { read_value ! ( $ iter , String ) . chars ( ) . map ( | c | ( c as u8 - $ base as u8 ) as usize ) . collect ::< Vec < usize >> ( ) } ; ( $ iter : expr , { char : $ base : expr } ) => { read_value ! ( $ iter , { chars : $ base } ) [ 0 ] } ; ( $ iter : expr , chars ) => { read_value ! ( $ iter , String ) . chars ( ) . collect ::< Vec < char >> ( ) } ; ( $ iter : expr , char ) => { read_value ! ( $ iter , chars ) [ 0 ] } ; ( $ iter : expr , usize1 ) => { read_value ! ( $ iter , usize ) - 1 } ; ( $ iter : expr , $ t : ty ) => { $ iter . next ( ) . unwrap ( ) . parse ::<$ t > ( ) . unwrap ( ) } ; }
pub struct UnionFind {
    parents: Vec<isize>,
}
use std::collections::HashMap;
impl UnionFind {
    pub fn new(n: usize) -> UnionFind {
        let parents = vec![-1; n];
        UnionFind { parents: parents }
    }
    pub fn find(&mut self, x: usize) -> usize {
        if self.parents[x] < 0 {
            x
        } else {
            let xx = self.parents[x] as usize;
            let y = self.find(xx);
            self.parents[x] = y as isize;
            y
        }
    }
    pub fn unite(&mut self, x: usize, y: usize) -> bool {
        use std::mem::swap;
        let mut x = self.find(x);
        let mut y = self.find(y);
        if x == y {
            return false;
        }
        if self.parents[x] > self.parents[y] {
            swap(&mut x, &mut y);
        }
        self.parents[x] += self.parents[y];
        self.parents[y] = x as isize;
        true
    }
    pub fn size(&mut self, x: usize) -> usize {
        let x = self.find(x);
        (-self.parents[x]) as usize
    }
    pub fn same(&mut self, x: usize, y: usize) -> bool {
        self.find(x) == self.find(y)
    }
    pub fn members(&mut self, x: usize) -> Vec<usize> {
        let root = self.find(x);
        (0..self.parents.len())
            .into_iter()
            .filter(|i| self.find(*i) == root)
            .collect::<Vec<usize>>()
    }
    pub fn roots(&mut self) -> Vec<usize> {
        (0..self.parents.len())
            .into_iter()
            .filter(|i| self.parents[*i] < 0)
            .collect::<Vec<usize>>()
    }
    pub fn all_group_members(&mut self) -> HashMap<usize, Vec<usize>> {
        let mut groups_map = HashMap::new();
        for x in 0..self.parents.len() {
            let r = self.find(x);
            groups_map.entry(r).or_insert(vec![]).push(x);
        }
        groups_map
    }
}
#[derive(Debug)]
pub struct Zarray {
    z: Vec<usize>,
}
impl Zarray {
    fn new<T: Eq>(s: &Vec<T>) -> Zarray {
        let n = s.len();
        let mut z = vec![0; n];
        let (mut i, mut j) = (1, 0);
        while i < n {
            while i + j < n && s[j] == s[i + j] {
                j += 1;
            }
            z[i] = j;
            if j == 0 {
                i += 1;
                continue;
            }
            let mut k = 1;
            while i + k < n && k + z[k] < j {
                z[i + k] = z[k];
                k += 1;
            }
            i += k;
            j -= k;
        }
        Zarray { z: z }
    }
    fn search<T: Eq>(s: &Vec<T>, pat: &Vec<T>, sep: T) -> Vec<usize> {
        let mut res = vec![];
        let mut t = vec![];
        t.extend(pat);
        t.push(&sep);
        t.extend(s);
        let zarray = Zarray::new(&t);
        for i in 0..t.len() {
            if zarray[i] == pat.len() {
                res.push(i - pat.len() - 1);
            }
        }
        res
    }
}
impl std::ops::Index<usize> for Zarray {
    type Output = usize;
    fn index(&self, u: usize) -> &usize {
        &self.z[u]
    }
}
fn main() {
    input! { s: chars, t: chars };
    let n = s.len();
    let m = t.len();
    let mut s2 = s.clone();
    while s2.len() < n + m - 1 {
        s2.extend(s.clone());
    }
    let mut a = vec![false; n];
    for i in Zarray::search(&s2, &t, '$').into_iter() {
        a[i % n] = true;
    }
    let mut uf = UnionFind::new(n);
    for i in 0..n {
        if a[i] {
            if uf.same(i, (i + m) % n) {
                println!("{}", -1);
                return;
            }
            uf.unite(i, (i + m) % n);
        }
    }
    println!("{}", (0..n).map(|i| uf.size(i)).max().unwrap() - 1);
}