#include <bits/stdc++.h>
using namespace std;
int prime = 31;
int maxn = 1000000 + 1;
vector<unsigned long long> powers;
vector<int> pos;
vector<unsigned long long> h;
unsigned long long MOD = 1000000000 + 7;
string t;
int m;
unsigned long long calc(int i, int j) {
  if (i == 0) return h[j];
  unsigned long long result = h[j] - h[i - 1];
  if (h[j] < h[i - 1]) result = h[j] + MOD - h[i - 1];
  return result % MOD;
}
int main() {
  powers.push_back(1);
  unsigned long long last = 1;
  for (int i = 1; i <= maxn; ++i) {
    last = (last * prime) % MOD;
    powers.push_back(last);
  }
  std::ios::sync_with_stdio(false);
  string s;
  cin >> s;
  int cnt0 = 0, cnt1 = 0;
  bool revert = false;
  if (s[0] == '1') revert = true;
  int n = s.length();
  pos.resize(n);
  for (int i = 0; i < n; ++i) {
    int k = (s[i] == '0') ? 0 : 1;
    if (revert) k = 1 - k;
    if (k == 0) {
      cnt0++;
      pos[i] = 0;
    } else {
      cnt1++;
      pos[i] = 1;
    }
  }
  cin >> t;
  m = t.length();
  h.resize(m, 0);
  h[0] = t[0] - 'a' + 1;
  for (int i = 1; i < m; ++i) {
    unsigned long long lll = powers[i] * (t[i] - 'a' + 1);
    lll = lll % MOD;
    h[i] = (h[i - 1] + lll) % MOD;
  }
  int total = 0;
  for (int len0 = 1; len0 < m; ++len0) {
    if (((long long)len0 * cnt0) > m) continue;
    int len1 = (m - len0 * cnt0) / cnt1;
    if ((long long)len0 * cnt0 + (long long)len1 * cnt1 != m) continue;
    if (len1 <= 0) continue;
    bool good = true;
    int left = 0;
    unsigned long long h0 = 0, h1 = 0;
    bool first0 = true, first1 = true;
    int p0 = 0, p1 = 0;
    for (int j = 0; j < n; ++j) {
      if (pos[j] == 0) {
        int right = left + len0 - 1;
        unsigned long long hh = calc(left, right);
        if (first0) {
          h0 = hh;
          p0 = right;
          first0 = false;
        } else {
          if (((h0 * powers[right]) % MOD) != ((hh * powers[p0]) % MOD)) {
            good = false;
            break;
          }
        }
        left += len0;
      } else {
        int right = left + len1 - 1;
        unsigned long long hh = calc(left, right);
        if (first1) {
          h1 = hh;
          p1 = right;
          first1 = false;
        } else {
          if (((h1 * powers[right]) % MOD) != ((hh * powers[p1]) % MOD)) {
            good = false;
            break;
          }
        }
        left += len1;
      }
    }
    if (good && ((h1 * powers[p0] % MOD) != (h0 * powers[p1]) % MOD)) {
      total++;
    }
  }
  cout << total << endl;
  return 0;
}

### Prompt

Please provide a cpp coded solution to the problem described below:

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;
int prime = 31;
int maxn = 1000000 + 1;
vector<unsigned long long> powers;
vector<int> pos;
vector<unsigned long long> h;
unsigned long long MOD = 1000000000 + 7;
string t;
int m;
unsigned long long calc(int i, int j) {
  if (i == 0) return h[j];
  unsigned long long result = h[j] - h[i - 1];
  if (h[j] < h[i - 1]) result = h[j] + MOD - h[i - 1];
  return result % MOD;
}
int main() {
  powers.push_back(1);
  unsigned long long last = 1;
  for (int i = 1; i <= maxn; ++i) {
    last = (last * prime) % MOD;
    powers.push_back(last);
  }
  std::ios::sync_with_stdio(false);
  string s;
  cin >> s;
  int cnt0 = 0, cnt1 = 0;
  bool revert = false;
  if (s[0] == '1') revert = true;
  int n = s.length();
  pos.resize(n);
  for (int i = 0; i < n; ++i) {
    int k = (s[i] == '0') ? 0 : 1;
    if (revert) k = 1 - k;
    if (k == 0) {
      cnt0++;
      pos[i] = 0;
    } else {
      cnt1++;
      pos[i] = 1;
    }
  }
  cin >> t;
  m = t.length();
  h.resize(m, 0);
  h[0] = t[0] - 'a' + 1;
  for (int i = 1; i < m; ++i) {
    unsigned long long lll = powers[i] * (t[i] - 'a' + 1);
    lll = lll % MOD;
    h[i] = (h[i - 1] + lll) % MOD;
  }
  int total = 0;
  for (int len0 = 1; len0 < m; ++len0) {
    if (((long long)len0 * cnt0) > m) continue;
    int len1 = (m - len0 * cnt0) / cnt1;
    if ((long long)len0 * cnt0 + (long long)len1 * cnt1 != m) continue;
    if (len1 <= 0) continue;
    bool good = true;
    int left = 0;
    unsigned long long h0 = 0, h1 = 0;
    bool first0 = true, first1 = true;
    int p0 = 0, p1 = 0;
    for (int j = 0; j < n; ++j) {
      if (pos[j] == 0) {
        int right = left + len0 - 1;
        unsigned long long hh = calc(left, right);
        if (first0) {
          h0 = hh;
          p0 = right;
          first0 = false;
        } else {
          if (((h0 * powers[right]) % MOD) != ((hh * powers[p0]) % MOD)) {
            good = false;
            break;
          }
        }
        left += len0;
      } else {
        int right = left + len1 - 1;
        unsigned long long hh = calc(left, right);
        if (first1) {
          h1 = hh;
          p1 = right;
          first1 = false;
        } else {
          if (((h1 * powers[right]) % MOD) != ((hh * powers[p1]) % MOD)) {
            good = false;
            break;
          }
        }
        left += len1;
      }
    }
    if (good && ((h1 * powers[p0] % MOD) != (h0 * powers[p1]) % MOD)) {
      total++;
    }
  }
  cout << total << endl;
  return 0;
}

```