#include <bits/stdc++.h>
using namespace std;
long long b1 = 127, b2 = 131, M1 = 1e9 + 7, M2 = 1e9 + 9;
const int MAX_N = 1e6 + 7;
long long h1[MAX_N], h2[MAX_N], pow1[MAX_N], pow2[MAX_N];
long long mod(long long x, long long m) {
  x %= m;
  if (x < 0) x += m;
  return x;
}
pair<long long, long long> get_substr_h(int l, int r) {
  return make_pair(mod(h1[r] - h1[l - 1] * pow1[r - l + 1], M1),
                   mod(h2[r] - h2[l - 1] * pow2[r - l + 1], M2));
}
int main() {
  srand(time(0));
  if (rand() % 2) swap(b1, b2);
  pow1[0] = pow2[0] = 1;
  for (int i = 1; i < MAX_N; i++) {
    pow1[i] = (pow1[i - 1] * b1) % M1;
    pow2[i] = (pow2[i - 1] * b2) % M2;
  }
  string s, t;
  cin >> s >> t;
  h1[0] = h2[0] = 0;
  for (int i = 1; i <= t.length(); i++) {
    h1[i] = (h1[i - 1] * b1 + (t[i - 1] - 'a' + 1)) % M1;
    h2[i] = (h2[i - 1] * b2 + (t[i - 1] - 'a' + 1)) % M2;
  }
  long long ans = 0, one = 0, zero = 0;
  for (int i = 0; i < s.length(); i++) {
    if (s[i] == '0')
      zero++;
    else
      one++;
  }
  for (long long l = 1; l < t.length(); l++) {
    if ((l * zero < t.length()) &&
        ((((int)t.length()) - l * zero) % one == 0)) {
      int r = (((int)t.length()) - l * zero) / one;
      pair<long long, long long> eq_h_zero = make_pair(-1, -1),
                                 eq_h_one = make_pair(-1, -1);
      int now_pos = 1;
      bool flag = 1;
      for (int i = 0; i < s.length(); i++) {
        if (s[i] == '0') {
          if (eq_h_zero == make_pair(-1ll, -1ll)) {
            eq_h_zero = get_substr_h(now_pos, now_pos + l - 1);
            now_pos += l;
            continue;
          }
          if (get_substr_h(now_pos, now_pos + l - 1) != eq_h_zero) {
            flag = 0;
            break;
          }
          now_pos += l;
        } else {
          if (eq_h_one == make_pair(-1ll, -1ll)) {
            eq_h_one = get_substr_h(now_pos, now_pos + r - 1);
            now_pos += r;
            continue;
          }
          if (get_substr_h(now_pos, now_pos + r - 1) != eq_h_one) {
            flag = 0;
            break;
          }
          now_pos += r;
        }
      }
      if (eq_h_zero == eq_h_one) flag = 0;
      if (flag) ans++;
    }
  }
  cout << ans << endl;
  return 0;
}

### Prompt

Please formulate 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;
long long b1 = 127, b2 = 131, M1 = 1e9 + 7, M2 = 1e9 + 9;
const int MAX_N = 1e6 + 7;
long long h1[MAX_N], h2[MAX_N], pow1[MAX_N], pow2[MAX_N];
long long mod(long long x, long long m) {
  x %= m;
  if (x < 0) x += m;
  return x;
}
pair<long long, long long> get_substr_h(int l, int r) {
  return make_pair(mod(h1[r] - h1[l - 1] * pow1[r - l + 1], M1),
                   mod(h2[r] - h2[l - 1] * pow2[r - l + 1], M2));
}
int main() {
  srand(time(0));
  if (rand() % 2) swap(b1, b2);
  pow1[0] = pow2[0] = 1;
  for (int i = 1; i < MAX_N; i++) {
    pow1[i] = (pow1[i - 1] * b1) % M1;
    pow2[i] = (pow2[i - 1] * b2) % M2;
  }
  string s, t;
  cin >> s >> t;
  h1[0] = h2[0] = 0;
  for (int i = 1; i <= t.length(); i++) {
    h1[i] = (h1[i - 1] * b1 + (t[i - 1] - 'a' + 1)) % M1;
    h2[i] = (h2[i - 1] * b2 + (t[i - 1] - 'a' + 1)) % M2;
  }
  long long ans = 0, one = 0, zero = 0;
  for (int i = 0; i < s.length(); i++) {
    if (s[i] == '0')
      zero++;
    else
      one++;
  }
  for (long long l = 1; l < t.length(); l++) {
    if ((l * zero < t.length()) &&
        ((((int)t.length()) - l * zero) % one == 0)) {
      int r = (((int)t.length()) - l * zero) / one;
      pair<long long, long long> eq_h_zero = make_pair(-1, -1),
                                 eq_h_one = make_pair(-1, -1);
      int now_pos = 1;
      bool flag = 1;
      for (int i = 0; i < s.length(); i++) {
        if (s[i] == '0') {
          if (eq_h_zero == make_pair(-1ll, -1ll)) {
            eq_h_zero = get_substr_h(now_pos, now_pos + l - 1);
            now_pos += l;
            continue;
          }
          if (get_substr_h(now_pos, now_pos + l - 1) != eq_h_zero) {
            flag = 0;
            break;
          }
          now_pos += l;
        } else {
          if (eq_h_one == make_pair(-1ll, -1ll)) {
            eq_h_one = get_substr_h(now_pos, now_pos + r - 1);
            now_pos += r;
            continue;
          }
          if (get_substr_h(now_pos, now_pos + r - 1) != eq_h_one) {
            flag = 0;
            break;
          }
          now_pos += r;
        }
      }
      if (eq_h_zero == eq_h_one) flag = 0;
      if (flag) ans++;
    }
  }
  cout << ans << endl;
  return 0;
}

```