#include <bits/stdc++.h>
using namespace std;
const int inv = 1000000000;
const int minv = -inv;
const int max_m = 100000 + 5;
const int max_n = 1000000 + 5;
const long long modref = ((long long)(1e9 + 7));
const long long base = 27ll;
const long long ibase = 370370373ll;
long long raise(long long a, int p) {
  if (p == 0) return 1ll;
  long long t = raise(a, p / 2);
  t = (t * t) % modref;
  if (p & 1) t = (t * a) % modref;
  return t;
}
int m, n;
char s[max_m], t[max_n];
long long phash[max_n + 1];
long long gethash(int l, int r) {
  long long diff = (phash[r] - phash[l] + modref) % modref;
  long long mul = raise(ibase, l);
  return (diff * mul) % modref;
}
int main() {
  scanf("%s", s);
  for (m = 0; s[m] != 13 and s[m] != 0; ++m)
    ;
  s[m] = 0;
  scanf("%s", t);
  for (n = 0; t[n] != 13 and t[n] != 0; ++n)
    ;
  t[n] = 0;
  if (s[0] == '1')
    for (int i = 0; i < m; ++i) s[i] = (s[i] == '0' ? '1' : '0');
  phash[0] = 0ll;
  long long basepow = 1ll;
  for (int i = 0; i < n; ++i) {
    phash[i + 1] =
        (phash[i] + ((long long)(t[i] - 'a' + 1)) * basepow) % modref;
    basepow = (basepow * base) % modref;
  }
  int c0 = 0, c1 = 0;
  for (int i = 0; i < m; ++i) {
    c0 += (s[i] == '0');
    c1 += (s[i] == '1');
  }
  int res = 0;
  for (int l0 = 1; l0 < n; ++l0) {
    if (l0 * c0 >= n) break;
    if ((n - (l0 * c0)) % c1 != 0) continue;
    int l1 = (n - (l0 * c0)) / c1;
    bool valid = true;
    int j = 0;
    long long hash0 = phash[l0], hash1;
    bool seen1 = false;
    for (int i = 0; i < m; ++i) {
      if (s[i] == '0') {
        if (gethash(j, j + l0) != hash0) {
          valid = false;
          break;
        }
        j += l0;
      } else {
        if (not seen1) {
          seen1 = true;
          hash1 = gethash(j, j + l1);
          if (hash0 == hash1) {
            valid = false;
            break;
          }
        } else {
          if (gethash(j, j + l1) != hash1) {
            valid = false;
            break;
          }
        }
        j += l1;
      }
    }
    res += valid;
  }
  printf("%d\n", res);
  return 0;
}

### Prompt

Your challenge is to write a Cpp solution to the following problem:

One of Arkady's friends works at a huge radio telescope. A few decades ago the telescope has sent a signal s towards a faraway galaxy. Recently they've received a response t which they believe to be a response from aliens! The scientists now want to check if the signal t is similar to s.

The original signal s was a sequence of zeros and ones (everyone knows that binary code is the universe-wide language). The returned signal t, however, does not look as easy as s, but the scientists don't give up! They represented t as a sequence of English letters and say that t is similar to s if you can replace all zeros in s with some string r_0 and all ones in s with some other string r_1 and obtain t. The strings r_0 and r_1 must be different and non-empty.

Please help Arkady's friend and find the number of possible replacements for zeros and ones (the number of pairs of strings r_0 and r_1) that transform s to t.

Input

The first line contains a string s (2 ≤ |s| ≤ 10^5) consisting of zeros and ones — the original signal.

The second line contains a string t (1 ≤ |t| ≤ 10^6) consisting of lowercase English letters only — the received signal.

It is guaranteed, that the string s contains at least one '0' and at least one '1'.

Output

Print a single integer — the number of pairs of strings r_0 and r_1 that transform s to t.

In case there are no such pairs, print 0.

Examples

Input


01
aaaaaa


Output


4


Input


001
kokokokotlin


Output


2

Note

In the first example, the possible pairs (r_0, r_1) are as follows:

  * "a", "aaaaa" 
  * "aa", "aaaa" 
  * "aaaa", "aa" 
  * "aaaaa", "a" 



The pair "aaa", "aaa" is not allowed, since r_0 and r_1 must be different.

In the second example, the following pairs are possible: 

  * "ko", "kokotlin" 
  * "koko", "tlin" 

### Response

```cpp
#include <bits/stdc++.h>
using namespace std;
const int inv = 1000000000;
const int minv = -inv;
const int max_m = 100000 + 5;
const int max_n = 1000000 + 5;
const long long modref = ((long long)(1e9 + 7));
const long long base = 27ll;
const long long ibase = 370370373ll;
long long raise(long long a, int p) {
  if (p == 0) return 1ll;
  long long t = raise(a, p / 2);
  t = (t * t) % modref;
  if (p & 1) t = (t * a) % modref;
  return t;
}
int m, n;
char s[max_m], t[max_n];
long long phash[max_n + 1];
long long gethash(int l, int r) {
  long long diff = (phash[r] - phash[l] + modref) % modref;
  long long mul = raise(ibase, l);
  return (diff * mul) % modref;
}
int main() {
  scanf("%s", s);
  for (m = 0; s[m] != 13 and s[m] != 0; ++m)
    ;
  s[m] = 0;
  scanf("%s", t);
  for (n = 0; t[n] != 13 and t[n] != 0; ++n)
    ;
  t[n] = 0;
  if (s[0] == '1')
    for (int i = 0; i < m; ++i) s[i] = (s[i] == '0' ? '1' : '0');
  phash[0] = 0ll;
  long long basepow = 1ll;
  for (int i = 0; i < n; ++i) {
    phash[i + 1] =
        (phash[i] + ((long long)(t[i] - 'a' + 1)) * basepow) % modref;
    basepow = (basepow * base) % modref;
  }
  int c0 = 0, c1 = 0;
  for (int i = 0; i < m; ++i) {
    c0 += (s[i] == '0');
    c1 += (s[i] == '1');
  }
  int res = 0;
  for (int l0 = 1; l0 < n; ++l0) {
    if (l0 * c0 >= n) break;
    if ((n - (l0 * c0)) % c1 != 0) continue;
    int l1 = (n - (l0 * c0)) / c1;
    bool valid = true;
    int j = 0;
    long long hash0 = phash[l0], hash1;
    bool seen1 = false;
    for (int i = 0; i < m; ++i) {
      if (s[i] == '0') {
        if (gethash(j, j + l0) != hash0) {
          valid = false;
          break;
        }
        j += l0;
      } else {
        if (not seen1) {
          seen1 = true;
          hash1 = gethash(j, j + l1);
          if (hash0 == hash1) {
            valid = false;
            break;
          }
        } else {
          if (gethash(j, j + l1) != hash1) {
            valid = false;
            break;
          }
        }
        j += l1;
      }
    }
    res += valid;
  }
  printf("%d\n", res);
  return 0;
}

```