#include <bits/stdc++.h>
using namespace std;
long long a[1345678], b[1456111], c[1211111], n, i, l,
    s = 0, k = 0, m1, m2, m, j, t, x, y, z, xx, yy, zz;
string p, q, r, rr;
int main() {
  cin >> p >> q;
  n = p.size();
  l = q.size();
  if (n > l) {
    cout << 0;
    return 0;
  }
  for (i = 0; i < n; i++) {
    if (p[i] == p[0]) x++;
  }
  z = 0;
  while (p[z] == p[0]) z++;
  y = n - x;
  m = 1000000007;
  m1 = 11881;
  b[0] = 1;
  m2 = 84168;
  c[0] = 1;
  for (i = 1; i < 1111111; i++) b[i] = b[i - 1] * m1 % m;
  for (i = 1; i < 1111111; i++) c[i] = c[i - 1] * m2 % m;
  for (i = 1; i <= l; i++) {
    a[i] = (a[i - 1] * m1 + q[i - 1]) % m;
  }
  for (i = 1; i < l; i++) {
    if (l <= i * x) break;
    if ((l - i * x) % y == 0) {
      k = i;
      t = (l - i * x) / y;
      xx = a[i];
      yy = (a[z * k + t] - (a[z * k] * b[t] % m) + m) % m;
      if (xx == yy) continue;
      zz = 0;
      long long urt = 0, shalga = 0;
      for (j = 0; j < n; j++) {
        if (p[j] == p[0]) {
          zz = (zz * b[k] + xx) % m;
          urt += k;
          if (zz != a[urt]) shalga = 1;
        } else {
          zz = (zz * b[t] + yy) % m;
          urt += t;
          if (zz != a[urt]) shalga = 1;
        }
      }
      if (shalga == 0) s++;
    }
  }
  cout << s << endl;
}

### Prompt

Please create a solution in Cpp 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;
long long a[1345678], b[1456111], c[1211111], n, i, l,
    s = 0, k = 0, m1, m2, m, j, t, x, y, z, xx, yy, zz;
string p, q, r, rr;
int main() {
  cin >> p >> q;
  n = p.size();
  l = q.size();
  if (n > l) {
    cout << 0;
    return 0;
  }
  for (i = 0; i < n; i++) {
    if (p[i] == p[0]) x++;
  }
  z = 0;
  while (p[z] == p[0]) z++;
  y = n - x;
  m = 1000000007;
  m1 = 11881;
  b[0] = 1;
  m2 = 84168;
  c[0] = 1;
  for (i = 1; i < 1111111; i++) b[i] = b[i - 1] * m1 % m;
  for (i = 1; i < 1111111; i++) c[i] = c[i - 1] * m2 % m;
  for (i = 1; i <= l; i++) {
    a[i] = (a[i - 1] * m1 + q[i - 1]) % m;
  }
  for (i = 1; i < l; i++) {
    if (l <= i * x) break;
    if ((l - i * x) % y == 0) {
      k = i;
      t = (l - i * x) / y;
      xx = a[i];
      yy = (a[z * k + t] - (a[z * k] * b[t] % m) + m) % m;
      if (xx == yy) continue;
      zz = 0;
      long long urt = 0, shalga = 0;
      for (j = 0; j < n; j++) {
        if (p[j] == p[0]) {
          zz = (zz * b[k] + xx) % m;
          urt += k;
          if (zz != a[urt]) shalga = 1;
        } else {
          zz = (zz * b[t] + yy) % m;
          urt += t;
          if (zz != a[urt]) shalga = 1;
        }
      }
      if (shalga == 0) s++;
    }
  }
  cout << s << endl;
}

```