#include <bits/stdc++.h>
using namespace std;
string s, t;
const long long p = 231;
long long ppow[3000000];
long long h[3000000];
long long MOD = 900000173;
bool check(int l0, int l1) {
  long long h0, h1;
  bool f0 = false, f1 = false;
  int pos = 0;
  for (char c : s) {
    long long t;
    if (c == '0') {
      t = h[pos + l0 - 1];
      if (pos) t -= h[pos - 1];
      if (t < 0) t += MOD;
      t *= ppow[2000000 + 10 - pos];
      t %= MOD;
    } else {
      t = h[pos + l1 - 1];
      if (pos) t -= h[pos - 1];
      if (t < 0) t += MOD;
      t *= ppow[2000000 + 10 - pos];
      t %= MOD;
    }
    if (c == '0') {
      if (!f0) {
        h0 = t;
        f0 = true;
      } else {
        if (h0 != t) return false;
      }
      pos += l0;
    } else {
      if (!f1) {
        h1 = t;
        f1 = true;
      } else {
        if (h1 != t) return false;
      }
      pos += l1;
    }
  }
  return h1 != h0;
}
int main() {
  ios_base::sync_with_stdio(false);
  cin >> s >> t;
  ppow[0] = 1;
  for (int i = 1; i < 3000000; i++) {
    ppow[i] = ppow[i - 1] * p;
    ppow[i] %= MOD;
  }
  h[0] = ppow[0] * t[0];
  for (int i = 1; i < t.size(); i++) {
    h[i] = h[i - 1] + ppow[i] * t[i];
    h[i] %= MOD;
  }
  int res = 0;
  int k0 = 0, k1 = 0;
  for (char c : s)
    if (c == '0')
      k0++;
    else
      k1++;
  if (k0 > k1) {
    for (int l0 = 1; l0 * k0 < t.length(); l0++) {
      if ((t.length() - l0 * k0) % k1 == 0) {
        int l1 = (t.length() - l0 * k0) / k1;
        if (check(l0, l1)) {
          res++;
        }
      }
    }
  } else {
    for (int l1 = 1; l1 * k1 < t.length(); l1++) {
      if ((t.length() - l1 * k1) % k0 == 0) {
        int l0 = (t.length() - l1 * k1) / k0;
        if (check(l0, l1)) {
          res++;
        }
      }
    }
  }
  cout << res << endl;
  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;
string s, t;
const long long p = 231;
long long ppow[3000000];
long long h[3000000];
long long MOD = 900000173;
bool check(int l0, int l1) {
  long long h0, h1;
  bool f0 = false, f1 = false;
  int pos = 0;
  for (char c : s) {
    long long t;
    if (c == '0') {
      t = h[pos + l0 - 1];
      if (pos) t -= h[pos - 1];
      if (t < 0) t += MOD;
      t *= ppow[2000000 + 10 - pos];
      t %= MOD;
    } else {
      t = h[pos + l1 - 1];
      if (pos) t -= h[pos - 1];
      if (t < 0) t += MOD;
      t *= ppow[2000000 + 10 - pos];
      t %= MOD;
    }
    if (c == '0') {
      if (!f0) {
        h0 = t;
        f0 = true;
      } else {
        if (h0 != t) return false;
      }
      pos += l0;
    } else {
      if (!f1) {
        h1 = t;
        f1 = true;
      } else {
        if (h1 != t) return false;
      }
      pos += l1;
    }
  }
  return h1 != h0;
}
int main() {
  ios_base::sync_with_stdio(false);
  cin >> s >> t;
  ppow[0] = 1;
  for (int i = 1; i < 3000000; i++) {
    ppow[i] = ppow[i - 1] * p;
    ppow[i] %= MOD;
  }
  h[0] = ppow[0] * t[0];
  for (int i = 1; i < t.size(); i++) {
    h[i] = h[i - 1] + ppow[i] * t[i];
    h[i] %= MOD;
  }
  int res = 0;
  int k0 = 0, k1 = 0;
  for (char c : s)
    if (c == '0')
      k0++;
    else
      k1++;
  if (k0 > k1) {
    for (int l0 = 1; l0 * k0 < t.length(); l0++) {
      if ((t.length() - l0 * k0) % k1 == 0) {
        int l1 = (t.length() - l0 * k0) / k1;
        if (check(l0, l1)) {
          res++;
        }
      }
    }
  } else {
    for (int l1 = 1; l1 * k1 < t.length(); l1++) {
      if ((t.length() - l1 * k1) % k0 == 0) {
        int l0 = (t.length() - l1 * k1) / k0;
        if (check(l0, l1)) {
          res++;
        }
      }
    }
  }
  cout << res << endl;
  return 0;
}

```