#include <bits/stdc++.h>
using namespace std;
const int N = 1e6 + 5, inf = 1e9 + 7;
int n, k, x, y, p, q;
string t, s;
int sa[N], pos[N], tmp[N], lcp[N], gap, f[N][20];
bool sufCmp(int i, int j) {
  if (pos[i] != pos[j]) return pos[i] < pos[j];
  i += gap;
  j += gap;
  return (i <= n && j <= n) ? pos[i] < pos[j] : i > j;
}
void create_SA() {
  n = t.size();
  for (int i = 1; i <= n; ++i) sa[i] = i, pos[i] = t[i - 1] - 'a' + 1;
  tmp[1] = 1;
  for (gap = 1;; gap *= 2) {
    sort(sa + 1, sa + n + 1, sufCmp);
    for (int i = 1; i <= n - 1; ++i)
      tmp[i + 1] = tmp[i] + sufCmp(sa[i], sa[i + 1]);
    for (int i = 1; i <= n; ++i) pos[sa[i]] = tmp[i];
    if (tmp[n] == n) break;
  }
}
void buildLCP() {
  for (int i = 1, k = 0; i <= n; ++i)
    if (pos[i] != n) {
      for (int j = sa[pos[i] + 1]; t[i + k - 1] == t[j + k - 1];) ++k;
      lcp[pos[i] + 1] = k;
      if (k) --k;
    }
}
int util(int a, int b) {
  if (a == b) return n - a;
  int x = min(abs(a - b), min(n - a, n - b));
  a = pos[a];
  b = pos[b];
  if (a > b) swap(a, b);
  int c = log2(b - a);
  return min(x, min(f[a][c], f[b - (1 << c)][c]));
}
signed main() {
  ios_base::sync_with_stdio(false);
  cin.tie(0);
  int i, j, a, b, ans = 0;
  cin >> s >> t;
  n = t.size();
  create_SA();
  buildLCP();
  for (i = 0; i < n; i++) f[i][0] = lcp[i + 2];
  for (i = 1; i < 20; i++) {
    for (j = 0; j < n; j++) {
      if (j + (1 << i) < n)
        f[j][i] = min(f[j][i - 1], f[j + (1 << i - 1)][i - 1]);
      else
        f[j][i] = f[j][i - 1];
    }
  }
  for (i = 1; i <= n; i++) pos[i - 1] = pos[i] - 1;
  for (i = 0; i < s.size(); i++) x += (s[i] == '0');
  y = s.size() - x;
  k = s.size();
  for (i = k - 1; i >= 0; i--) {
    if (s[i] == '0') p = i;
    if (s[i] == '1') q = i;
  }
  for (i = 1; i * x < n; i++)
    if ((n - x * i) % y == 0) {
      int l1 = i, l2 = (n - i * x) / y, c = 0, s1 = p * l2, s2 = q * l1;
      if (l1 == l2 && util(s1, s2) >= l1) continue;
      for (j = 0; j < k; j++) {
        if (s[j] == '0') {
          if (util(c, s1) < l1) break;
          c += l1;
        } else {
          if (util(c, s2) < l2) break;
          c += l2;
        }
      }
      if (c == n) ans++;
    }
  cout << ans;
}

### Prompt

In cpp, your task is to solve 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 N = 1e6 + 5, inf = 1e9 + 7;
int n, k, x, y, p, q;
string t, s;
int sa[N], pos[N], tmp[N], lcp[N], gap, f[N][20];
bool sufCmp(int i, int j) {
  if (pos[i] != pos[j]) return pos[i] < pos[j];
  i += gap;
  j += gap;
  return (i <= n && j <= n) ? pos[i] < pos[j] : i > j;
}
void create_SA() {
  n = t.size();
  for (int i = 1; i <= n; ++i) sa[i] = i, pos[i] = t[i - 1] - 'a' + 1;
  tmp[1] = 1;
  for (gap = 1;; gap *= 2) {
    sort(sa + 1, sa + n + 1, sufCmp);
    for (int i = 1; i <= n - 1; ++i)
      tmp[i + 1] = tmp[i] + sufCmp(sa[i], sa[i + 1]);
    for (int i = 1; i <= n; ++i) pos[sa[i]] = tmp[i];
    if (tmp[n] == n) break;
  }
}
void buildLCP() {
  for (int i = 1, k = 0; i <= n; ++i)
    if (pos[i] != n) {
      for (int j = sa[pos[i] + 1]; t[i + k - 1] == t[j + k - 1];) ++k;
      lcp[pos[i] + 1] = k;
      if (k) --k;
    }
}
int util(int a, int b) {
  if (a == b) return n - a;
  int x = min(abs(a - b), min(n - a, n - b));
  a = pos[a];
  b = pos[b];
  if (a > b) swap(a, b);
  int c = log2(b - a);
  return min(x, min(f[a][c], f[b - (1 << c)][c]));
}
signed main() {
  ios_base::sync_with_stdio(false);
  cin.tie(0);
  int i, j, a, b, ans = 0;
  cin >> s >> t;
  n = t.size();
  create_SA();
  buildLCP();
  for (i = 0; i < n; i++) f[i][0] = lcp[i + 2];
  for (i = 1; i < 20; i++) {
    for (j = 0; j < n; j++) {
      if (j + (1 << i) < n)
        f[j][i] = min(f[j][i - 1], f[j + (1 << i - 1)][i - 1]);
      else
        f[j][i] = f[j][i - 1];
    }
  }
  for (i = 1; i <= n; i++) pos[i - 1] = pos[i] - 1;
  for (i = 0; i < s.size(); i++) x += (s[i] == '0');
  y = s.size() - x;
  k = s.size();
  for (i = k - 1; i >= 0; i--) {
    if (s[i] == '0') p = i;
    if (s[i] == '1') q = i;
  }
  for (i = 1; i * x < n; i++)
    if ((n - x * i) % y == 0) {
      int l1 = i, l2 = (n - i * x) / y, c = 0, s1 = p * l2, s2 = q * l1;
      if (l1 == l2 && util(s1, s2) >= l1) continue;
      for (j = 0; j < k; j++) {
        if (s[j] == '0') {
          if (util(c, s1) < l1) break;
          c += l1;
        } else {
          if (util(c, s2) < l2) break;
          c += l2;
        }
      }
      if (c == n) ans++;
    }
  cout << ans;
}

```